Dividing Fractions in Word Problems
This Grade 6 math skill from Pengi Math (Grade 6) teaches students to apply fraction division to solve real-world word problems. Students interpret division situations involving fractions, set up the division equation, and solve by multiplying by the reciprocal, connecting math operations to practical scenarios.
Key Concepts
Property To solve word problems that involve splitting a total fractional amount into smaller, equal fractional parts, you set up a division expression. The total amount is the dividend and the size of the smaller part is the divisor. Total Amount $\div$ Size of Each Part = Number of Parts.
Examples A recipe calls for $\frac{1}{4}$ cup of sugar, but you only have a measuring scoop that holds $\frac{1}{8}$ of a cup. How many scoops of sugar do you need? $$ \frac{1}{4} \div \frac{1}{8} = \frac{1}{4} \times \frac{8}{1} = \frac{8}{4} = 2 \text{ scoops} $$ A plank of wood is $\frac{9}{10}$ of a meter long. How many pieces can be cut from it if each piece needs to be $\frac{3}{20}$ of a meter long? $$ \frac{9}{10} \div \frac{3}{20} = \frac{9}{10} \times \frac{20}{3} = \frac{180}{30} = 6 \text{ pieces} $$.
Explanation Word problems often describe real world situations where you need to divide fractions. To solve these, you must first identify which quantity is being divided (the dividend) and what size you are dividing it by (the divisor). Key phrases like "how many groups of... are in..." or "splitting... into equal parts of..." signal that division is needed. Once you have set up the division expression, you solve it by multiplying the first fraction by the reciprocal of the second.
Common Questions
How do you solve a word problem involving fraction division?
Identify what is being divided and by what, write the division expression with fractions, then multiply by the reciprocal of the divisor to find the answer.
What is a real-world example of dividing fractions?
If you have 3/4 of a pizza and want to divide it into portions of 1/8 each, you divide 3/4 ÷ 1/8 = 3/4 × 8 = 6 portions.
Why do you multiply by the reciprocal when dividing fractions?
Dividing by a fraction is the same as multiplying by its reciprocal because inverting and multiplying is the mathematical equivalent of fraction division.
How do you know which fraction is the divisor in a word problem?
The divisor is the size of each part or the number you are dividing by. Look for phrases like per, each, in every, or divided by in the problem.
Where is dividing fractions in word problems taught?
This skill is covered in the Grade 6 Pengi Math textbook under fraction operations.