# Fractions - Addition & Subtraction

The learning objectives are:

1. Relating fractions and division
3. Subtraction of mixed numbers
4. Simple word problems involving addition and subtraction of mixed numbers

## 1. Relating Fractions And Division

Fraction is related to division.

\begin{align*} \frac {1} {3} \end{align*} is the same as \begin{align*} 1 \div 3 \end{align*}.

Question 1:

Express each of the following as a fraction.

1.  \begin{align*} 3 \div 5 =\text{__________} \end{align*}

2. \begin{align*} 5 \div 9 = \text{__________} \end{align*}

3. \begin{align*} 6 \div 11 = \text{__________} \end{align*}

Solution:

1. \begin{align*} 3 \div 5 =\frac {3}{5} \end{align*}

2. \begin{align*} 5 \div 9 = \frac {5}{9} \end{align*}

3. \begin{align*} 6 \div 11 = \frac {6}{11} \end{align*}

Question 2:

Mary bought 2 pies. She divided it equally among her 3 children. What fraction of a pie did each child receive?

Solution:

Fraction of a pie each child received \begin{align*} =2 \div 3 \end{align*}

\begin{align*} = \frac {2}{3} \end{align*}

\begin{align*} \frac {2}{3} \end{align*}

Question 3:

Jack baked 15 muffins and shared them equally with 6 friends. What fraction of the muffins did each of them receive?

Solution:

Total muffins baked = 15 muffins

Total number of friends including Jack = 7

15 muffins are shared equally among 7 people.

Method 1:

Fraction of muffins received by each friend \begin{align*} = 15 \div 7 \end{align*}

\begin{align*} &=\frac {15} {7} \\ \\ &=2\frac {1} {7}\\ \end{align*}

Method 2:

\begin{align*} 2 \frac {1}{7} \end{align*}

## 2. Addition Of Mixed Numbers

To do addition of mixed numbers, we do the following steps:

Step 1:

Step 2:

Ensure that the denominators are the same. Make the denominators the same if they are not.

Step 3:

Step 4:

Simplify and express as a mixed number if possible.

Question 1:

\begin{align*} 2\frac { 2} { 5} + 5\frac {1 } {5 } \end{align*}

Solution:

\begin{align*} 2\frac { 2} { 5} + 5\frac {1 } {5 } &= 7\frac { 2} { 5} + \frac {1 } {5 }\\ \\ &= 7\frac { 3} { 5} \\ \end{align*}

Question 2:

\begin{align*} 1\frac {7} {10} + 6\frac {9} {10} \end{align*}

Solution:

\begin{align*} 1\frac { 7} { 10} + 6\frac {9 } {10 } &= 7\frac { 7} { 10} + \frac {9 } {10 }\\ \\ &= 7\frac { 16} { 10} \\ \\ &= 8\frac { 6} { 10} \\ \\ &= 8\frac { 3} { 5} \\ \end{align*}

\begin{align*} 8\frac { 3} { 5} \end{align*}

Question 3:

\begin{align*} 2\frac {3} {4} + 3\frac {5} {6} \end{align*}

Solution:

\begin{align*} 2\frac { 3} { 4} + 3\frac {5 } {6} &= 5\frac { 3} { 4} + \frac {5 } {6 }\\ \\ &= 5\frac { 9} { 12} + \frac {10 } {12 }\\ \\ &= 5\frac { 19} { 12} \\ \\ &= 6\frac { 7} { 12} \\ \end{align*}

\begin{align*} 6\frac { 7} { 12} \end{align*}

Question 4:

\begin{align*} 1\frac {6} {7} + 5\frac {9} {14} \end{align*}

Solution:

\begin{align*} 1\frac { 6} { 7} + 5\frac {9 } {14} &= 6\frac { 6} { 7} + \frac {9 } {14 }\\ \\ &= 6\frac { 12} { 14} + \frac { 9} { 14}\\ \\ &= 6\frac { 21} { 14} \\ \\ &= 7\frac { 7} { 14} \\ \\ &= 7\frac { 1} { 2} \\ \end{align*}

\begin{align*} 7\frac { 1} { 2} \end{align*}

## 3. Subtraction Of Mixed Numbers

To do addition of mixed numbers, we do the following steps:

Step 1:

Subtract the whole numbers.

Step 2:

Ensure that the denominators are the same. Make the denominators the same if they are not.

Step 3:

Rename the first mixed number if the numerators cannot be subtracted.

Step 4:

Subtract the fractions.

Step 5:

Simplify and express as a mixed number if possible.

Question 1:

Subtract the following.

\begin{align*} 5\frac {5} {6} - 1\frac {1} {3} \end{align*}

Solution:

\begin{align*} 5\frac {5} {6} - 1\frac {1} {3} &= 4\frac { 5} { 6} - \frac {1 } {3 }\\ \\ &= 4\frac { 5} { 6} - \frac {2 } {6 }\\ \\ &= 4\frac { 3} { 6} \\ \\ &= 4\frac { 1} { 2} \\ \end{align*}

\begin{align*} 4\frac { 1} { 2} \end{align*}

Question 2:

Subtract the following.

\begin{align*} 7\frac {3} {8} - 6\frac {7} {8} \end{align*}

Solution:

\begin{align*} 7\frac {3} {8} - 6\frac {7} {8} &= 1\frac { 3} { 8} - \frac {7 } {8 }\\ \\ &= \frac { 11} { 8} - \frac {7 } {8 }\\ \\ &= \frac { 4} { 8} \\ \\ &= \frac { 1} { 2} \\ \end{align*}

Alternatively, convert both fractions to improper fractions.

\begin{align*} 7\frac {3} {8} - 6\frac {7} {8} &= \frac { 59} { 8} - \frac {55} {8 }\\ \\ &= \frac { 4} { 8} \\ \\ &= \frac { 1} { 2} \\ \end{align*}

\begin{align*} \frac {1} {2} \end{align*}

Question 3:

Subtract the following.

\begin{align*} 6\frac {3} {10} - 1\frac {1} {2} \end{align*}

Solution:

\begin{align*} 6\frac {3} {10} - 1\frac {1} {2} &= 5\frac { 3} { 10} - \frac {1} {2}\\ \\ &= 5\frac { 3} { 10} - \frac {5} {10} \\ \\ &= 4\frac { 13} { 10} - \frac {5} {10} \\ \\ &= 4\frac { 8} { 10} \\ \\ &= 4\frac { 4} { 5} \\ \end{align*}

Alternatively, convert both fractions to improper fractions.

\begin{align*} 6\frac {3} {10} - 1\frac {1} {2} &= \frac { 63} { 10} - \frac {3} {2}\\ \\ &= \frac { 63} { 10} - \frac {15} {10} \\ \\ &= \frac {48} { 10} \\ \\ &= 4\frac { 8} { 10} \\ &= 4\frac { 4} { 5} \\ \end{align*}

\begin{align*} 4\frac { 4} { 5} \end{align*}

Question 4:

Subtract the following.

\begin{align*} 5\frac {7} {10} - 3\frac {3} {4} \end{align*}

Solution:

\begin{align*} 5\frac { 7 } { 10 } - 3 \frac { 3 } { 4 } &= 2 \frac { 7 } { 10 } - \frac { 3 } { 4 }\\ \\ &= 2 \frac { 14 } { 20 } - \frac { 15 } { 10 } \\ \\ &= 1 \frac { 34 } { 20 } - \frac { 15 } { 10 }\\ \\ &= 1\frac { 19 } { 20 } \\ \end{align*}

\begin{align*} 1\frac { 19 } { 20 } \end{align*}

## 4. Simple Word Problems Involving Addition And/or Subtraction Of Mixed Numbers

Question 1:

Jane had \begin{align*} 2\frac { 3 } { 5 }\; \text {kg} \end{align*} of coffee powder. Sarah has \begin{align*} 1\frac { 1 } { 5 } \; \text {kg} \end{align*} of coffee powder more than Jane. How much coffee powder does Sarah have?

Solution:

Mass of coffee powder Sarah has \begin{align*} = 2 \frac { 3 } { 5 } \; \text {kg} + 1\frac { 1 } { 5 } \;\text {kg} \end{align*}

\begin{align*} = 3 \frac { 4 } { 5 } \; \text {kg} \end{align*}

\begin{align*} 3 \frac { 4 } { 5 } \; \text {kg} \end{align*}

Question 2:

Mrs Tan had \begin{align*} 5\frac { 1 } { 2 }\; \text {kg} \end{align*} of flour. She had \begin{align*} 2\frac { 5 } { 6 }\; \text {kg} \end{align*} of flour more than Mrs Loh. How much flour did they have altogether?

Solution:

Mass of flour Mrs Loh had \begin{align*} = 5\frac { 1 } { 2 }\; \text {kg} - 2\frac { 5 } { 6 }\; \text {kg} \end{align*}

\begin{align*} &= 3\frac { 1 } { 2 }\; \text {kg} - \frac { 5 } { 6 }\; \text {kg} \\ \\ &= 3\frac { 3 } { 6 }\; \text {kg} - \frac { 5 } { 6 }\; \text {kg} \\ \\ &= 2\frac { 9 } { 6 }\; \text {kg} - \frac { 5 } { 6 }\; \text {kg} \\ \\ &= 2\frac { 4 } { 6 }\; \text {kg} \\ \\ &= 2\frac { 2 } { 3 }\; \text {kg} \\ \end{align*}

Total mass of flour they had \begin{align*} = 5\frac { 1 } { 2 }\; \text {kg} + 2\frac { 2 } { 3 }\; \text {kg} \end{align*}

\begin{align*} &= 7\frac { 1 } { 2 }\; \text {kg} + \frac { 2 } { 3 }\; \text {kg} \\ \\ &= 7\frac { 3 } { 6 }\; \text {kg} + \frac { 4 } { 6 }\; \text {kg} \\ \\ &= 7\frac { 7 } { 6 }\; \text {kg} \\ \\ &= 8\frac { 1 } { 6 }\; \text {kg} \\ \end{align*}

\begin{align*} 8\frac { 1 } { 6 }\; \text {kg} \end{align*}

Question 3:

Sandy had \begin{align*} 3\frac { 1 } { 2 }\; \text {kg} \end{align*} of sugar. She had \begin{align*} 2\frac { 5 } { 6 }\; \text {kg} \end{align*} of sugar less than Amy. How many kilograms of sugar did they have altogether?

Solution:

Mass of sugar Amy had \begin{align*} = 3\frac { 1 } { 2 }\; \text {kg} + 2\frac { 5 } { 6 }\; \text {kg} \end{align*}

\begin{align*} &= 5\frac { 1 } { 2 }\; \text {kg} + \frac { 5 } { 6 }\; \text {kg} \\ \\ &= 5\frac { 3 } { 6 }\; \text {kg} + \frac { 5 } { 6 }\; \text {kg} \\ \\ &= 5\frac { 8 } { 6 }\; \text {kg} \\ \\ &= 6\frac { 2 } { 6 }\; \text {kg} \\ \\ &= 6\frac { 1 } { 3 }\; \text {kg} \\ \end{align*}

Total mass of sugar Sandy and Amy had \begin{align*} = 3\frac { 1 } { 2 }\; \text {kg} + 6\frac { 1 } { 3 }\; \text {kg} \end{align*}

\begin{align*} &= 9\frac { 1 } { 2 }\; \text {kg} + \frac { 1 } { 3 }\; \text {kg} \\ \\ &= 9\frac { 3 } { 6 }\; \text {kg} + \frac { 2 } { 6 }\; \text {kg} \\ \\ &= 9\frac { 5 } { 6 }\; \text {kg} \\ \\ \end{align*}

\begin{align*} 9\frac { 5 } { 6 }\; \text {kg} \end{align*}

## Conclusion

In this article, we have learnt about Addition and Subtraction of Fractions as per the Primary 5 Math level. We have learnt the following subtopics in fractions.

• Relating fractions and division
• Subtraction of mixed numbers
• Simple word problems involving addition and subtraction of mixed numbers
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