# Mass

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

## 1. 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?

Solution:

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.

Container C is the lightest.

Question 2:

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.

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.

 C , B , A Lightest Heaviest

Question 3:

Which object is the heaviest?

Solution:

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.

Container C is the heaviest.

Question 4:

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 $+ \;350 \text{ g}$
$= 200 \text{ g} + 350 \text{ g}$
$= 550 \text{ g}$

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:

$2 \text{ kg} = 2000 \text{ g}$

$2000 \text{ g}$

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}

$3500 \text{ g}$

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}

$5027 \text{ g}$

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}

$3052 \text{ g}$

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}

$1300 \text{ g}$

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}

$7006 \text{ g}$

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}

$6020 \text{ g}$

Question 8:

Express the following in kilograms and grams.

$3000 \text{ g} =$  __________ $\text{ kg}$

Solution:

$3000 \text{ g} = 3 \text{ kg}$

$3 \text{ kg}$

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}

$4 \text{ kg } 800 \text{ g}$

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}

$2 \text{ kg } 500 \text{ g}$

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}

$3 \text{ kg } 70 \text{ g}$

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}

$5 \text{ kg } 900 \text{ g}$

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}

$4 \text{ kg } 85 \text{ g}$

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}

$7 \text{ kg } 707 \text{ g}$

## 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:

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}

(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}

(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}

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:

$3 \text{ g},\; 300 \text{ g},\; 3 \text{ kg},\; 3 \text{ kg } 30 \text{ g}$

$3 \text{ g},\; 300 \text{ g},\; 3 \text{ kg},\; 3 \text{ kg } 30 \text{ g}$

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,

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

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

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,

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

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

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:

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

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

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,

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

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

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,

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

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

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

Ivan is the heaviest.

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