Explanations
Explain what equivalent fractions are and how you can find one.
Equivalent fractions represent the same value. Multiply or divide the numerator and denominator by the same non-zero number.
I said 3/4 + 2/4 = 5/8. What did I do wrong?
Added the denominators: you should only add numerators: 3/4 + 2/4 = 5/4.
Convert 9/4 to a mixed number
2 and 1/4
Convert 3 3/8 to an improper fraction
27/8
Sarah ate 1/4 of a pizza, and Ben ate 2/4. How much did they eat in total?
1/4 + 2/4 = 3/4 of the pizza.
Why do we find a common denominator when adding or subtracting fractions, but not when multiplying?
For addition/subtraction, parts must be the same size.
I said 3/2 = 11/2
Error in converting improper fraction. Correct: 3/2 = 1 and 1/2.
2/5 + 7/10 = ?
2/5 = 4/10 → 4/10 + 7/10 = 11/10 = 1 and 1/10.
3/5 + 4/10 = ?
3/5 + 2/5 = 1
One machine paints 5/8 of a wall per hour. A second machine paints 3/8 per hour. How long together to finish one wall?
5/8 + 3/8 = 1 wall/hour → 1 hour to finish.
Explain the difference between a mixed number and an improper fraction.
A mixed number has a whole number and a fraction (e.g., 2½). An improper fraction has a numerator larger than the denominator (e.g., 5/2).
4/5 − 2/3 = 2/2
Didn’t use common denominators. LCD = 15 → 12/15 − 10/15 = 2/15
4/9 × 3/8 = ?
12/72 = 1/6
1 and 4/5 - 7/9
1 and 4/5 = 9/5 → 9/5 - 7/9 = 81/45 - 35/45 = 46/45 → 1 and 1/45
A soccer player runs 2/3 of a kilometre in each lap. How far after 1 1/2 laps?
1 1/2 = 3/2 → 2/3 × 3/2 = 1 km.
What does the term reciprocal mean, and when do we use it?
The reciprocal flips the numerator and denominator; we use it when dividing by fractions.
5/6 ÷ 1/3 = 5/18
Didn’t flip the divisor. Should be 5/6 × 3/1 = 15/6 = 2 1/2
5/6 × 3/8 = ?
15/48 = 5/16
7/9 ÷ 2/3 = ?
7/9 × 3/2 = 21/18 = 7/6 = 1 1/6
A recipe calls for 2 1/4 cups of sugar. You only have 3/4 of a cup. What fraction of the recipe can you make?
3/4 ÷ 9/4 = 3/4 × 4/9 = 12/36 = 1/3 of the recipe.
When dividing by a fraction, why do we “flip” the second fraction and multiply?
Because you can't have a denominator as a fraction, you have to make it a whole number. when we multiply the denominator by the reciprocal, the answer is always one, a whole number. And remember, whatever we do the denominator, we have to do the numerator.
When comparing 3/4 and 5/6, I said 3/4 is greater because 3 < 5
You can’t compare only numerators. LCD = 12 → 9/12 < 10/12, so 5/6 is greater
(5/6 ÷ 2/5) − 1/3 = ?
5/6 × 5/2 = 25/12, then 25/12 − 4/12 = 21/12 = 7/4 = 1 and 3/4.
(1/2)2 + 1/3 = ?
(1/2)2 → 1/2 x 1/2 =1/4 →1/4 + 1/3= 3/12 + 4/12 = 7/12
A board is 2 and 1/2 metres long. You need pieces that are 3/8 metre each. How many full pieces can you cut?
2 and1/2 = 5/2 → 5/2 ÷ 3/8 = 5/2 × 8/3 = 40/6 = 6 2/3 → 6 full pieces.