Adding and subtracting fractions with the same denominator booklet
Adding and subtracting fractions with the same denominator booklet
- Unit 1: Numbers
- Unit 2: Geometry and measure
- Unit 3 : Statistics and probability
🎯 In this topic you will
- Add fractions that have the same denominator.
- Subtract fractions that have the same denominator.
- Work out fraction answers that are greater than one whole.
🧠 Key Words
- improper fraction
- proper fraction
Show Definitions
- improper fraction: A fraction where the numerator is equal to or greater than the denominator, so the value is one or more than one whole.
- proper fraction: A fraction where the numerator is smaller than the denominator, so the value is less than one whole.
🍰 Sharing a Cake
A cake is divided into five equal pieces. Two people each take one piece, and we want to find out what fraction of the cake is left. Fractions can be used to describe how much of the whole cake remains after some pieces have been taken.
How to work it out: $1 - \dfrac{2}{5} = \dfrac{3}{5}$
📘 Building on What You Know
I n Stage 3, you worked with fractions that stayed within one whole. In this unit, you will extend that understanding by adding and subtracting fractions where the total can be greater than one.
❓ EXERCISES
$1.$ The chef serves $\frac{1}{6}$ of an apple pie. What fraction of the apple pie is left?
👀 Show answer
$2.$ Copy and complete these calculations.
$a.$ $\frac{3}{4} + \square = 1$
$b.$ $1 - \square = \frac{1}{8}$
👀 Show answer
$3.$ For each grid write down the pairs of fractions that add up to $1$. For each pair of fractions, write two subtraction sentences.
👀 Show answer
$\frac{1}{2} + \frac{1}{2} = 1$, $\;1 - \frac{1}{2} = \frac{1}{2}$, $\;1 - \frac{1}{2} = \frac{1}{2}$
$\frac{4}{5} + \frac{1}{5} = 1$, $\;1 - \frac{4}{5} = \frac{1}{5}$, $\;1 - \frac{1}{5} = \frac{4}{5}$
$\frac{3}{4} + \frac{1}{4} = 1$, $\;1 - \frac{3}{4} = \frac{1}{4}$, $\;1 - \frac{1}{4} = \frac{3}{4}$
$\frac{2}{3} + \frac{1}{3} = 1$, $\;1 - \frac{2}{3} = \frac{1}{3}$, $\;1 - \frac{1}{3} = \frac{2}{3}$
$4.$ Work out these calculations.
$a.$ $\frac{5}{9} + \frac{5}{9}$
$b.$ $\frac{4}{5} - \frac{1}{5}$
$c.$ $\frac{6}{7} - \frac{3}{7}$
$d.$ $\frac{5}{12} - \frac{1}{12}$
👀 Show answer
$5.$ In the diagram, the fraction in each box is the sum of the two fractions below it. Copy the diagram and fill in the missing fractions.
👀 Show answer
Top box: $\frac{10}{9}$
$6.$ Yuri adds two fractions. This is his working.
$\frac{3}{9} + \frac{2}{9} = \frac{5}{18}$
Yuri is not correct. Explain what he has done wrong. What is the correct answer?
👀 Show answer
Correct answer: $\frac{3}{9} + \frac{2}{9} = \frac{5}{9}$
$7.$ Fatima and Parveen work out the answer to $\frac{4}{5} + \frac{3}{5}$. Fatima says the answer is $\frac{7}{5}$. Parveen says the answer is $\frac{7}{10}$. Who do you agree with? Explain your answer.
👀 Show answer
$\frac{4}{5} + \frac{3}{5} = \frac{7}{5}$
🧠 Think like a Mathematician
a. Draw a square of edge $2\,\text{cm}$ on square spotty paper.
b. Join any two dots on the perimeter (outside edge) with a straight line to split the square into two pieces. What fraction of the whole have you split the square into?
c. Record your results as a calculation, for example:
$\frac{7}{8} + \frac{1}{8} = 1$
d. Find as many different ways as possible to split the square into two pieces.
👀 Show answer
- When a straight line joins two points on the perimeter, the square is divided into two regions whose areas add up to the whole square.
- The fractions will always sum to $1$, for example $\frac{1}{2} + \frac{1}{2} = 1$, $\frac{3}{4} + \frac{1}{4} = 1$, or $\frac{7}{8} + \frac{1}{8} = 1$, depending on where the line is drawn.
- Different choices of perimeter points create different fractional splits, but in every case the two fractions represent complementary parts of the same whole.
💡 Quick Math Tip
Fractions that make a whole: When a shape is split into two parts, the fractions of the two pieces must always add up to $1$, even if the pieces are different sizes.