Topics
5. Fractions
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AustraliaNSW
Stage 3

5.15 Compare and write add and subtract sentences

Lesson
Practice
Lesson

Are you ready?

Remembering how to  add and subtract fractions  is going to help us in this lesson. Let's try this problem to review.

Examples

Example 1

Find the value of \dfrac{4}{7} - \dfrac{3}{7}.

Worked Solution
Create a strategy

Subtract the numerators since both these fractions have the same denominator.

Apply the idea
\displaystyle \dfrac{4}{7} - \dfrac{3}{7}\displaystyle =\displaystyle \dfrac{4-3}{7}Subtract the numerators
\displaystyle =\displaystyle \dfrac{1}{7}
Idea summary

Adding or subtracting fractions with the same denominator is very similar to adding or subtracting with whole numbers. The difference is we are counting fraction parts instead.

Compare fraction statements

This video will look at how to compare statements using the less than and greater than symbols.

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Examples

Example 2

Write the symbol, >, \, <, or =, to make the statement true.\dfrac{5}{19} + \dfrac{6}{19}\, ⬚ \,\dfrac{7}{19}

Worked Solution
Create a strategy

Add the fractions on the left-side and compare it to the fraction on the right-side.

Apply the idea
Two circles with plus sign in between. Each is divided into 19 equal parts. First circle has 5 shaded parts, the other has 6.

Here is the area model of the left hand side, \dfrac{5}{19} + \dfrac{6}{19}. We can see that there are 5+6=11 shaded parts in total.

\displaystyle \dfrac{5}{19} + \dfrac{6}{19}\displaystyle =\displaystyle \dfrac{5+6}{19}Add the numerators
\displaystyle =\displaystyle \dfrac{11}{19}
A circles divided into 19 equal parts with 7 shaded parts.

Here is the area model of the right hand side, \dfrac{7}{19}.

Since \dfrac{11}{19} \gt \dfrac{7}{19}. This means that:\dfrac{5}{19} + \dfrac{6}{19} > \dfrac{7}{19}

Idea summary

When comparing fractions, if the denominators are the same, then we can compare the numerators.

Compare mixed numbers

This video will show us how to compare statements that have mixed numbers.

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Examples

Example 3

Write the symbol, >, \, <, or =, to make the statement true.1 \dfrac{2}{6} + 3 \dfrac{3}{6} \, ⬚ \, 4 \dfrac{4}{6}

Worked Solution
Create a strategy

Add the mixed numbers on the left-side and compare it to the fraction on the right-side.

Apply the idea

On the left side we have 1\dfrac{2}{6} + 3\dfrac{3}{6}.

Adding the wholes together, we get 1+3=4, which is the same as the whole number part on the right side. So we can just compare the fractional parts to complete the statement.

\displaystyle 1\dfrac{2}{6} + 3\dfrac{3}{6}\displaystyle =\displaystyle 1 + 3 +\dfrac{2}{6}+\dfrac{3}{6} Group the whole numbers and fractions
\displaystyle =\displaystyle 4 +\frac{5}{6} Add the whole numbers and the fractions
\displaystyle =\displaystyle 4\frac{5}{6} Write as a mixed number

Since \dfrac{5}{6} > \dfrac{4}{6}, we know that 4\dfrac{5}{6} > 4\dfrac{4}{6}.

So the statement is:1 \dfrac{2}{6} + 3 \dfrac{3}{6} \, > \, 4 \dfrac{4}{6}

Idea summary

When comparing mixed numbers which have equal whole number parts, we can just compare the fractional parts.

Number sentences with fractions

Now we will look at writing number sentences from story problems.

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Examples

Example 4

Paul had travelled one eighth of the distance to school when he realised he had forgotten his squash racquet and so went home to get it.

Complete the number sentence that describes how far in total Paul has travelled by the time he arrives back at home:

Paul has travelled ⬚ eighth plus ⬚ eighth of the distance between his home and school.

Worked Solution
Create a strategy

Find the fraction that Paul had travelled to school and back to his home.

Apply the idea

The fraction of the way to school that Paul had already travelled when he turned back is 1 eighth.

Paul will travel exactly the same distance on the way back.

That is, Paul will first travel one eighth and then one eighth again. We can add these fractions together to make the total distance that Paul travels.

So we have the number sentence:

Paul has travelled 1 eighth plus 1 eighth of the distance between his home and school.

Idea summary

Underline the key words in the story to help understand the mathematics.

A number sentence is a way to represent the mathematics with symbols.

Outcomes

MA3-7NA

compares, orders and calculates with fractions, decimals and percentages

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