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Here are a few recommended readings before getting started with this lesson.
Paulina runs for two-sixths of her free time each day.
If Paulina has 5 hours of free time per day, how many hours does she run in 4 days? Give the exact answer.
The product of two fractions is equal to the product of the numerators divided by the product of the denominators. The resulting fraction is then simplified to its lowest terms, if possible.
ba⋅dc=b⋅da⋅c
Paulina drinks one-third of the water in her bottle before PE class. During class, she drinks ten-twelfths of the remaining water.
Notice that each third is divided into six smaller equal parts. The other third can also be divided into six parts. This will make it easier to find what fraction of the whole the red part represents.
The red part shows what fraction of the water bottle Paulina drinks during class.
Rewrite | Compare with 21, or 126 | |
---|---|---|
1210 | 1210 | 1210>126 |
32 | 3⋅42⋅4=128 | 128>126 |
Estimate for 1210×32 | |
---|---|
Round 1210 to 1 | 1×32=32 |
Round 32 to 1 | 1210×1=1210 |
The fraction 1210 can be simplified to 65. The answer is either 32 or 65. The fractions in the options are in simplest form and 32 is among the options. Therefore, the answer is 32.
The numerators determine which parts will be shaded. Since 10 is the numerator of 1210, 10 of the 12 columns will be shaded. Similarly, 2 of the 3 rows will be shaded.
In this model, the overlapping region represents the product. For this example, the product is 3620=95.
The product of two fractions is equal to the product of the numerators divided by the product of the denominators. Practice finding the product of fractions. Simplify the answer to its lowest terms.
When multiplying fractions by whole numbers or mixed numbers, both factors should be in the form of a proper fraction or an improper fraction.
Rewrite 9 as 19
ba=b/9a/9
Simplify quotient
Rewrite 19 as 15+4
Write as a sum of fractions
Calculate quotient
Rewrite 1+154 as 1154
Paulina's PE class lasts for 1125 hours. The table shows what fraction of the class time is allocated for various activities.
Activity | Fraction |
---|---|
Warm-up | 51 |
Instruction | 21 |
Playing a game | 101 |
Cool-down | 51 |
Part of 1125-hour Class | ||
---|---|---|
Activity | Fraction | |
Warm-up | 51 | |
Instruction | 21 | |
Playing game | 101 | |
Cool-down | 51 |
Rewrite 60 as 160
Multiply fractions
Multiply
Calculate quotient
Part of 1125-hour Class | ||
---|---|---|
Activity | Fraction | |
Warm-up | 51 | |
Instruction | 21 | |
Playing game | 101 | |
Cool-down | 51 |