Grade 6 (age 11-12)

Fraction Division

Dividing by a fraction means flipping the divisor and multiplying. Dividing one half by one quarter just counts how many quarters fit inside one half. Think of splitting half a pizza into quarter slices to get two pieces. Here you drag the numerators and denominators to see why flip and multiply works.

Why Multiply by the Reciprocal?

🍕 Division as Counting Groups

①Sharing 3/4 of a pizza in 1/3-pizza portions

②Count how many 1/3 fit in 3/4

③Counting directly matches "flip and multiply"!

Verify Visually

Dividend numerator3

Dividend denominator4

Divisor numerator1

Divisor denominator3

Summary

Fraction Division = Multiply by Reciprocal

ab ÷ cd = ab × dc = a × db × c

Swap numerator and denominator of the divisor and multiply

Whole ÷ Fraction

n ÷ ab = n × ba = n × ba

Treat whole numbers as n/1

🎯 Key Points

①Division = flip and multiply

②Reciprocal: swap top and bottom (reciprocal of 2/3 is 3/2)

③Dividing by a number less than 1 makes the result larger

④Reduce after multiplying

⑤Check: quotient × divisor = dividend

Examples & Unit Review

Example 1

Calculate 2/3 ÷ 4/5.

To divide fractions, flip the second fraction and multiply: 2/3 ÷ 4/5 = 2/3 × 5/4.

Multiply numerators and denominators: (2×5)/(3×4) = 10/12 = 5/6.

▸ 5/6

The key is to turn division into multiplication and flip the second fraction.

Example 2

Calculate 3/4 ÷ 6.

Treat the whole number 6 as 6/1; flipping gives 1/6: 3/4 ÷ 6 = 3/4 × 1/6.

(3×1)/(4×6) = 3/24 = 1/8.

▸ 1/8

When dividing by a whole number, multiply the denominator by that number.

Unit Review

What is 5/6 ÷ 2/3?

①5/4

②5/9

③4/5

④9/5

▸ ① 5/4

Change division to multiplication: 5/6 ÷ 2/3 = 5/6 × 3/2.

(5×3)/(6×2) = 15/12 = 5/4.

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Decimal Division