Fractions of a whole (age 10+)
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b); solve word problems involving division of whole numbers leading to fractional or mixed-number answers
What a learner can do afterwards
- Explain that 3/4 means 3 ÷ 4 and verify by showing 3/4 × 4 = 3
- Solve: '9 people share a 50-pound sack equally — how many pounds each?' and express the answer as 5 5/9
- Use a visual model to show that sharing 3 wholes among 4 people gives each person 3/4
The lesson
A fraction like 3/4 is really a division hiding in plain sight. It means 3 ÷ 4: three things shared equally among four people. Whatever number sits on top gets divided by whatever number sits on bottom.
Nine friends share a 50-pound sack of rice equally. Since 50 ÷ 9 does not come out even, divide with a remainder first: 50 ÷ 9 = 5 remainder 5. That leftover 5 pounds still gets split 9 ways, so each person gets 5 and 5/9 pounds.
You can check any fraction-as-division answer by multiplying back. Since 3 ÷ 4 = 3/4, multiply 3/4 by 4 and you should land back on 3. It works, because the parts recombine into the wholes you started with.
A fraction a/b always means a ÷ b, and multiplying the fraction by b brings you back to a.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.