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Mass

In this article, we will look at the following:

  1. Comparison of mass given balance scales
  2. Conversion of mass
  3. Comparison of mass

1. Comparison Of Mass Given Balance Scales

Comparison Of Mass Given Balance Scales

From the diagram, we know that:

  1. Container A is lighter than Container B.
  2. Container B is heavier than Container A.

Question 1:

Which container is the lightest?

Which container is the lightest?

Solution:  

To find the lightest container, we cross out all the heavier containers on each scale.

To find the lightest container, we cross out all the heavier containers on each scale.

We cross out  Container B on the first balance, Container A on the second balance and Container D on the third balance.

We are then left with Container A on the first balance, and Container C on the second and third balance.

Since Container A was crossed out, we know that Container C is the lightest.

Answer:

Container C is the lightest.

 

Question 2:

Arrange the objects in order, beginning with the lightest.

Arrange the objects in order, beginning with the lightest.

Solution:

To find the lightest object, we cross out the heavier objects on the 2 balances.

To find the lightest object, we cross out the heavier objects on the 2 balances.

We cross out  Object A on the first balance and Object B on the second balance.

Hence, C is the lightest.

To find the heaviest object, we cross out the lighter objects on the 2 balances.

We cross out Object B  on the first balance and Object C on the second balance.

Hence, Object A  is the heaviest.

Answer:

C

,

B

,

A

Lightest

 

 

 

Heaviest

 

Question 3:

Which object is the heaviest?

Which object is the heaviest?

Solution:

To find the heaviest object, we cross out the lighter objects on the balances.

To find the heaviest object, we cross out the lighter objects on the balances.

We cross out Object B on the first and the second balances and Object A on the last balance.

As shown on the third balance, Object B and Object D have the same mass.

Hence, Object C  is the heaviest.

Answer: 

Container C is the heaviest.

 

Question 4:

Which object is the heaviest?

Which object is the heaviest?

Solution:

Mass of Object A \(= 350 \text{ g}\)

Mass of Object B \(= 200 \text{ g}\)

Mass of Object C \(=\) Mass of Object B \(+ \;350 \text{ g}\)
                                \(                             = 200 \text{ g} + 350 \text{ g}\)
                                \(= 550 \text{ g}\)

Answer:

Container C is the heaviest. 

 

2. Conversion Of Mass

To express mass in kilograms to grams and vice versa, we need to remember that:

\(1 \text{ kg} = 1000 \text{ g}\)

Question 1:

Express the following in grams.

\(2 \text{ kg } =\) __________ \(\text{ g}\)

Solution:

\(2 \text{ kg} = 2000 \text{ g}\)

Answer: 

\(2000 \text{ g}\)

 

Question 2:

Express the following in grams.

\(3 \text{ kg } 500 \text{ g} =\)__________ \(\text{ g}\)

Solution:

\(\begin{align} 3 \text{ kg } 500 \text{ g} &= 3000 \text{ g} + 500 \text{ g}\\ &= 3500 \text{ g} \end{align}\)

Answer:

\(3500 \text{ g}\)

 

Question 3:

Express the following in grams.

\(5 \text{ kg } 27 \text{ g} =\)__________ \(\text{ g}\)

Solution:

\(\begin{align} 5 \text{ kg } 27 \text{ g} &= 5000 \text{ g} + 27 \text{ g}\\ &= 5027 \text{ g} \end{align}\)

Answer:

\(5027 \text{ g}\)

 

Question 4:

Express the following in grams.

\(3 \text{ kg } 52 \text{ g} =\)__________ \(\text{ g}\)

Solution:

\(\begin{align} 3 \text{ kg } 52 \text{ g} &= 3000 \text{ g} + 52 \text{ g}\\ &= 3052 \text{ g} \end{align}\)

Answer:

\(3052 \text{ g}\)

 

Question 5:

Express the following in grams.

\(1 \text{ kg } 300 \text{ g} =\)__________ \(\text{ g}\)

Solution:

\(\begin{align} 1 \text{ kg } 300 \text{ g} &= 1000 \text{ g} + 300 \text{ g}\\ &= 1300 \text{ g} \end{align}\)

Answer:

\(1300 \text{ g}\)

 

Question 6:

Express the following in grams.

\(7 \text{ kg } 6 \text{ g} =\)__________ \(\text{ g}\)

Solution:

\(\begin{align} 7 \text{ kg } 6 \text{ g} &= 7000 \text{ g} + 6 \text{ g} \\ &= 7006 \text{ g} \end{align}\)

 Answer:

\(7006 \text{ g}\)

 

Question 7:

Express the following in grams.

\(6 \text{ kg } 20 \text{ g} =\)__________ \(\text{ g}\)

Solution:

\(\begin{align} 6 \text{ kg } 20 \text{ g} &= 6000 \text{ g} + 20 \text{ g}\\ &= 6020 \text{ g} \end{align}\)

Answer:

\(6020 \text{ g}\)

 

Question 8:

Express the following in kilograms and grams.

\(3000 \text{ g} =\)  __________ \(\text{ kg} \)

Solution:

\(3000 \text{ g} = 3 \text{ kg} \)

Answer:

\(3 \text{ kg}\)

 

Question 9:

Express the following in kilograms and grams.

\(4800 \text{ g} =\)__________ \(\text{ kg}\) __________ \(\text{ g}\)

Solution:

\(\begin{align} 4800 \text{ g} &= 4000 \text{ g} + 800 \text{ g} \\ &= 4 \text{ kg } 800 \text{ g} \end{align}\)

Answer:

\(4 \text{ kg } 800 \text{ g}\)

 

Question 10:

Express the following in kilograms and grams.

\(2500 \text{ g} =\)__________ \(\text{ kg}\) __________ \(\text{ g}\)

Solution:

\(\begin{align} 2500 \text{ g} &= 2000 \text{ g} + 500 \text{ g}\\ &= 2 \text{ kg } 500 \text{ g} \end{align}\)

Answer: 

\(2 \text{ kg } 500 \text{ g}\)

 

Question 11:

Express the following in kilograms and grams.

\(3070 \text{ g} =\)__________ \(\text{ kg}\) __________ \(\text{ g}\)

Solution:

\(\begin{align} 3070 \text{ g} &= 3000 \text{ g} + 70 \text{ g}\\ &= 3 \text{ kg } 70 \text{ g} \end{align}\)

Answer:

\(3 \text{ kg } 70 \text{ g}\)

 

Question 12:

Express the following in kilograms and grams.

\(5900 \text{ g} =\)__________ \(\text{ kg}\) __________ \(\text{ g}\)

Solution:

\(\begin{align} 5900 \text{ g} &= 5000 \text{ g} + 900 \text{ g}\\ &= 5 \text{ kg } 900 \text{ g} \end{align}\)

Answer:

\(5 \text{ kg } 900 \text{ g}\)

 

Question 13:

Express the following in kilograms and grams.

\(4085 \text{ g} =\)__________ \(\text{ kg}\) __________ \(\text{ g}\)

Solution:

\(\begin{align} 4085 \text{ g} &= 4000 \text{ g} + 85 \text{ g}\\ &= 4 \text{ kg } 85 \text{ g} \end{align}\)

Answer:

\(4 \text{ kg } 85 \text{ g}\)

 

Question 14:

Express the following in kilograms and grams.

\(7707 \text{ g } =\)__________ \(\text{ kg}\) __________ \(\text{ g}\)

Solution:

\(\begin{align} 7707 \text{ g} &= 7000 \text{ g} + 707 \text{ g}\\ &= 7 \text{ kg } 707 \text{ g}  \end{align}\)

Answer:

\(7 \text{ kg } 707 \text{ g}\)

 

3. Comparison Of Mass

When comparing masses, we express them in the same units first ie: grams before comparing.

Question 1:

Study the pictures carefully:

Study the pictures carefully: Which is heavier?

Which is heavier?

Solution:  

The mass of the rock is \(1 \text{ kg}\). The mass of the cotton is \(1 \text{ kg}\).

Hence, both objects have the same mass.

 

Question 2:

Which of the following is the lightest?

  1. \(1 \text{ kg } 100 \text{ g}\)
  2. \(1 \text{ kg } 10 \text{ g}\)
  3. \(1 \text{ kg } 1 \text{ g}\)
  4. \(10 \,000 \text{ g} \)

Solution:

Express in grams before comparing.

\(\begin{align} 1 \text{ kg } 100 \text{ g} &= 1000 \text{ g} + 100 \text{ g}\\ &= 1100 \text{ g}\\[2ex] 1 \text{ kg } 10 \text{ g} &= 1000 \text{ g} + 10 \text{ g}\\ &= 1010 \text{ g}\\[2ex] 1 \text{ kg } 1 \text{ g} &= 1000 \text{ g} + 1 \text{ g}\\ &= 1001 \text{ g} \end{align}\)

Answer:

(3) \(1 \text{ kg } 1 \text{ g}\)

 

Question 3:

Which of the following is the heaviest?

  1. \(4 \text{ kg } 3 \text{ g}\)
  2. \(4 \text{ kg } 30 \text{ g}\)
  3. \(4 \text{ kg } 33 \text{ g}\)
  4. \(4 \text{ kg } 303 \text{ g}\)

Solution:

Express in grams before comparing.

\(\begin{align} 4 \text{ kg } 3 \text{ g} &= 4000 \text{ g} + 3 \text{ g}\\ &= 4003 \text{ g}\\[2ex] 4 \text{ kg } 30 \text{ g} &= 4000 \text{ g} + 30 \text{ g}\\ &= 4030 \text{ g}\\[2ex] 4 \text{ kg } 33 \text{ g} &= 4000 \text{ g} + 33 \text{ g}\\ &= 4033 \text{ g}\\[2ex] 4 \text{ kg } 303 \text{ g} &= 4000 \text{ g} + 303 \text{ g}\\ &= 4303 \text{ g} \end{align}\)

Answer:

(4) \(4 \text{ kg } 303 \text{ g}\)

 

Question 4:

Which one of the following is the heaviest?

  1. A sack of potatoes weighs \(4 \text{ kg } 404 \text{ g}\).
  2. A cat weighs \(4 \text{ kg } 440 \text{ g}\).
  3. A watermelon weighs \(4 \text{ kg } 444 \text{ g}\).
  4. A lamp weighs \(4 \text{ kg } 4 \text{ g}\).

Solution:

Express in grams before comparing.

Mass of the sack of potatoes
\(\begin{align}&= 4000 \text{ g} + 404 \text{ g}\\[2ex] &= 4404 \text{ g} \end{align}\)

Mass of the cat
\(\begin{align}&= 4000 \text{ g} + 440 \text{ g}\\[2ex] &= 4440 \text{ g} \end{align}\)

Mass of the watermelon
\(\begin{align}&= 4000 \text{ g} + 444 \text{ g}\\[2ex] &= 4444 \text{ g} \end{align}\)

Mass of the lamp
\(\begin{align} &= 4000 \text{ g} + 4 \text{ g}\\[2ex] &= 4004 \text{ g} \end{align}\)

Answer:

3) The watermelon is the heaviest.

 

Question 5:

Arrange the following in ascending order.

\(3 \text{ kg},\; 3 \text{ g},\; 3 \text{ kg } 30 \text{ g},\; 300 \text{ g}\)

Solution:

Ascending order means from the smallest to the greatest.
So, we arrange the following from the lightest to the heaviest.

Express in grams before comparing.

\(\begin{align} 3 \text{ kg } &= 3000 \text{ g}\\[2ex] 3 \text{ kg } 30 \text{ g} &= 3000 \text{ g} + 30 \text{ g}\\ &= 3030 \text{ g} \end{align}\)

Arranging them in ascending order:

\(3 \text{ g},\; 300 \text{ g},\; 3 \text{ kg},\; 3 \text{ kg } 30 \text{ g}\)

Answer:

\(3 \text{ g},\; 300 \text{ g},\; 3 \text{ kg},\; 3 \text{ kg } 30 \text{ g}\)

 

Question 6:

Arrange the following in ascending order.

\(3 \text{ kg } 50 \text{ g},\; 3440 \text{ g},\; 3 \text{ kg } 450 \text{ g},\; 3045 \text{ g}\)

Solution:

\(\begin{align} 3 \text{ kg } 50 \text{ g} &= 3000 \text{ g} + 50 \text{ g}\\ &= 3050 \text{ g}\\[2ex] 3 \text{ kg } 450 \text{ g} &= 3000 \text{ g} + 450 \text{ g}\\ &= 3450 \text{ g} \end{align}\)

Arranging the following in ascending order,

\(3045 \text{ g},\; 3 \text{ kg } 50 \text{ g},\; 3440 \text{ g},\; 3 \text{ kg } 450 \text{ g}\)

Answer:

\(3045 \text{ g},\; 3 \text{ kg } 50 \text{ g},\; 3440 \text{ g},\; 3 \text{ kg } 450 \text{ g}\)

 

Question 7:

Arrange the following in ascending order.

\(2 \text{ kg } 20 \text{ g},\; 2200 \text{ g},\; 2002 \text{ g},\; 2 \text{ kg } 202 \text{ g}\)

Solution:

\(\begin{align} 2 \text{ kg } 20 \text{ g} &= 2000 \text{ g} + 20 \text{ g}\\ &= 2020 \text{ g}\\[2ex] 2 \text{ kg } 202 \text{ g} &= 2000 \text{ g} + 202 \text{ g}\\ &= 2202 \text{ g} \end{align}\)

Arranging the following in ascending order,

\(2002 \text{ g},\; 2 \text{ kg } 20 \text{ g},\; 2200 \text{ g},\; 2 \text{ kg } 202 \text{ g}\)

Answer:

\(2002 \text{ g},\; 2 \text{ kg } 20 \text{ g},\; 2200 \text{ g},\; 2 \text{ kg } 202 \text{ g}\)

 

Question 8:

Arrange the following in descending order.

\(770 \text{ g},\; 7770 \text{ g},\; 7 \text{ kg } 707 \text{ g},\; 707 \text{ g}\)

Solution:

Descending order means from the greatest to the smallest.
So, we arrange the following from the heaviest to the lightest.

Express in grams before comparing.

\(\begin{align} 7 \text{ kg } 707 \text{ g} &= 7000 \text{ g} + 707 \text{ g}\\ &= 7707 \text{ g} \end{align}\)

Arranging them in descending order:

\(7770 \text{ g},\; 7 \text{ kg } 707 \text{ g},\; 770 \text{ g},\; 707 \text{ g}\)

Answer:

\(7770 \text{ g},\; 7 \text{ kg } 707 \text{ g},\; 770 \text{ g},\; 707 \text{ g}\)

 

Question 9:

Arrange the following in descending order.

\(1 \text{ kg } 10 \text{ g},\; 1100 \text{ g},\; 101 \text{ g},\; 1 \text{ kg } 101 \text{ g}\)

Solution:

\(\begin{align} 1 \text{ kg } 10 \text{ g} &= 1000 \text{ g} + 10 \text{ g}\\ &= 1010 \text{ g}\\[2ex] 1 \text{ kg } 101 \text{ g} &= 1000 \text{ g} + 101 \text{ g}\\ &= 1101 \text{ g} \end{align}\)

Arranging the following in descending order,

\(1 \text{ kg } 101 \text{ g},\; 1100 \text{ g},\; 1 \text{ kg } 10 \text{ g},\; 101 \text{ g}\)

Answer:

\(1 \text{ kg } 101 \text{ g},\; 1100 \text{ g},\; 1 \text{ kg } 10 \text{ g},\; 101 \text{ g}\)

 

Question 10:

Arrange the following in descending order.

\(66 \text{ kg } 606 \text{ g}, \;66 \text{ kg } 660 \text{ g},\; 66 \,006 \text{ g},\; 66 \,666 \text{ g}\)

Solution:

\(\begin{align} 66 \text{ kg } 606 \text{ g} &= 66 \,000 \text{ g} + 606 \text{ g}\\  &= 66 \,606 \text{ g}\\[2ex] 66 \text{ kg } 660 \text{ g} &= 66 \,000 \text{ g} + 660 \text{ g}\\ &= 66 \,660 \text{ g} \end{align}\)

Arranging the following in descending order,

\(66 \,666 \text{ g},\; 66 \text{ kg } 660 \text{ g},\; 66 \text{ kg } 606 \text{ g},\; 66 \,006 \text{ g}\)

Answer:

\(66 \,666 \text{ g},\; 66 \text{ kg } 660 \text{ g},\; 66 \text{ kg } 606 \text{ g},\; 66 \,006 \text{ g}\)

 

Question 11:

Alan is heavier than Owen but lighter than Ivan. 

Kimberly is lighter than Alan but heavier than Owen.

Who is the heaviest?

Solution:

In the first statement: Ivan is the heaviest while Owen is the lightest.
Arranging from the lightest to the heaviest,
Owen, Alan, Ivan

In the second statement: Alan is the heaviest while Owen is the lightest.
Arranging from the lightest to the heaviest,
Owen, Kimberly, Alan

Combining information from both statements:
Arranging from the lightest to the heaviest,
Owen, Kimberly, Alan, Ivan

Answer:

Ivan is the heaviest.

 

Continue Learning
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Length Area and Perimeter
Parallel And Perpendicular Lines  

 

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