PSHS NCE Fractions Reviewer

TEACHER ABI PSHS NCE · QUANTITATIVE ABILITY

Fractions

Compare fractions, find equivalent forms, solve operations, and use fraction sense to avoid common traps.

Grade 6–7 friendlyWorked examplesRegular practiceQuick Fire + Mastery

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Fractions

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A fraction tells you how many equal parts

3/4

The bottom number, 4, tells how many equal parts make one whole. The top number, 3, tells how many of those parts we have.

Important: The size of a fraction depends on both numbers. A bigger denominator does not automatically mean a bigger fraction.

1/2 = 2/4 = 3/6
These are equivalent fractions.

3/4 > 2/3
You can compare by using common denominators or cross-products.

DO IT FAST

Know the job before you calculate

1. Compare: Use common denominators or cross-multiply.
2. Add/Subtract: Make denominators the same first.
3. Multiply: Multiply straight across, then simplify.
4. Divide: Keep the first fraction, change ÷ to ×, flip the second fraction.
5. Check: Ask whether your answer should be smaller or larger than the numbers you started with.

WORKED EXAMPLES

Six patterns you should recognize

1. Equivalent fractions

Which fraction is equal to 3/5?

3/5 × 2/2 = 6/10

6/10

2. Compare fractions

Which is greater: 3/4 or 2/3?

3 × 3 = 9    and    2 × 4 = 8

3/4 is greater.

3. Add unlike fractions

1/3 + 1/4

4/12 + 3/12 = 7/12

7/12

4. Subtract fractions

5/6 − 1/4

10/12 − 3/12 = 7/12

7/12

5. Multiply fractions

3/5 × 10/9

30/45 = 2/3

Faster: simplify before multiplying when possible.

6. Divide fractions

2/3 ÷ 4/5

2/3 × 5/4 = 10/12 = 5/6

5/6

TRY WITH ME

Which is bigger?

Compare 5/8 and 3/5.

1. Cross-multiply: 5 × 5 = 25.
2. Then 3 × 8 = 24.
3. Compare 25 and 24.

5/8 is greater than 3/5. Since 25 > 24, the first fraction is larger.

COMMON TRAPS

Watch out for these

Adding denominators.
1/3 + 1/3 is 2/3, not 2/6.

Forgetting to simplify.
6/8 should become 3/4.

Flipping the wrong fraction.
When dividing, flip only the second fraction.

Assuming a larger denominator means a larger fraction.
For unit fractions, the opposite is true: 1/8 is smaller than 1/4.

REGULAR PRACTICE

Build the skill

These mix equivalence, comparison, operations, and fraction word problems.

QUICK FIRE

Can you spot it fast?

Five short questions. Use the fastest valid method.

Question 1 of 5

FRESH MASTERY CHECK

Can you do it without hints?

Score 5/5 to verify this competency. If you miss one, a fresh set will be ready.

NEED HELP?

Fractions still getting mixed up?

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