Dividing Fractions Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
A container holds 910\frac{9}{10} of a litre of juice. Each glass holds 320\frac{3}{20} of a litre. How many full glasses can be filled?

Solution

  1. 1
    Set up the division: 910÷320\frac{9}{10} \div \frac{3}{20}.
  2. 2
    Multiply by the reciprocal: 910×203\frac{9}{10} \times \frac{20}{3}.
  3. 3
    Cancel common factors: 910×203=9×2010×3=18030=6\frac{9}{10} \times \frac{20}{3} = \frac{9 \times 20}{10 \times 3} = \frac{180}{30} = 6.

Answer

6 full glasses6 \text{ full glasses}
Dividing by a fraction answers 'how many of this size fit in that amount?' Flipping the divisor and multiplying (keep-change-flip) converts the problem into a standard multiplication, and cross-cancellation keeps the arithmetic tidy.

About Dividing Fractions

Dividing by a fraction means multiplying by its reciprocal: ab÷cd=ab×dc=adbc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}. This works because division asks 'how many groups of this size fit?'

Learn more about Dividing Fractions →

More Dividing Fractions Examples

Example 1 easy

Divide [formula].

Example 2 medium

A ribbon is [formula] of a metre long. It is cut into pieces that are each [formula] of a metre. How

Example 3 easy

Compute [formula].

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