In this lesson we solve fraction divisions by thinking how countless times the divisor "fits" or "goes into" the dividend. Because that example, the portion 1/4 goes into five 20 times, for this reason 5 ÷ (1/4) = 20. The lesson has lots of exercises v visual models and many word problems. The ahead lesson had to carry out with splitting fractions by totality numbers.In the video, I explain two different department situations whereby we don"t have to use the "rule" or shortcut for fraction division, but instead deserve to use mental math. The very first is once a portion is separated by a entirety number. The second is once the answer come a fraction department is a entirety number.
You are watching: How many times does 4 go into 21
How countless times walk one thing fit right into another?You can constantly write a division from this situation. Think: “How numerous times walk the divisor go into the dividend?” | |||
How many times does | go into | ? |
Eight times. We can write a division: 2 ÷ | 1 4 | = 8. |
Then examine the division: 8 × | 1 4 | = | 8 4 | = 2. |
1 2 | go into | 3? |
Six times. We have the right to write a division: 3 ÷ | 1 2 | = 6. |
Then inspect the division: 6 × | 1 2 | = | 6 2 | = 3. |
1.Solve. Write a division. Then compose a multiplication the checks her division.
a.How many times does |
| go into | ? |
2 ÷ | 1 3 | =_____ |
Check: ____ × | 1 3 | = |
go into | ? |
1 ÷ | 1 4 | = _____ |
Check: ____ × | 1 4 | = |
go into | ? |
6 ÷ | 1 3 | =____ |
go into | ? |
5 ÷ | 1 4 | =____ |
e. How plenty of times does | go right into | ? |
____ | ÷ | = |
go into | ? |
____ | ÷ | ____ | = |
1 6 | go right into 2? |
____ | ÷ | ____ | = |
1 5 | go right into 3? |
____ | ÷ | ____ | = |
a. 3 ÷ | 1 6 | = |
1 9 | = |
1 8 | = |
1 2 | = |
1 7 | = |
1 5 | = |
1 3 | = |
Did you notice a pattern? over there is a shortcut to separating a whole number by a unit fraction! | ÷ | 1 4 | |
↓ | ↓ | ||
5 | × | 4 | = 20 |
÷ | 1 8 | ||
↓ | ↓ | ||
3 | × | 8 | = 24 |
÷ | 1 7 | ||
↓ | ↓ | ||
9 | × | 7 | = 63 |
Why go it work that way? because that example, take into consideration the trouble 5 ÷ (1/4). Because 1/4 goesinto 1 precisely 4 times, that must enter 5 precisely 5 × 4 = 20 times.
3.Solve. Usage the shortcut.
a. 3 ÷ | 1 6 | = |
1 5 | = |
1 10 | = |
1 10 | = |
1 4 | = |
1 8 | = |
1 10 | = |
1 8 | = |
4. Compose a department for every word problem, and solve. Execute not write simply the answer.
a. How many 1/2-meter pieces deserve to you reduced from a role of string the is 6 meters long? |
b. How numerous 1/4-cup servings can you gain from 2 cup of almonds? |
c. Ben has tiny weights that weigh 1/10 kg each. How numerous of those would he should make 5 kg? |
d.An eraser is 1/8 customs thick. How numerous erasers deserve to be stacked right into a 4-inch tall box? |
a. 2 ÷ | 1 2 | = |
b. 5 ÷ | 1 3 | = |
6. These departments are not as easy as the previous ones, however they room not daunting either. Again, think how many times the divisor goes into the dividend. The pictures deserve to help.
a. 4 ÷ | 2 3 | = |
4 5 | = |
5 6 | ÷ | 1 6 | = |
6 10 | = |
5 9 | ÷ | 4 9 | = |
4 8 | ÷ | 5 8 | = |
7. Compose a department and solve. Write also a multiplication to examine your division.
a. How countless times does | go into | ? |
÷ | ____ | = | ____ |
× | ____ | = | ____ |
go into | ? |
÷ | ____ | = | ____ |
× | ____ | = | ____ |
go into | ? |
÷ | ____ | = | ____ |
× | ____ | = | ____ |
go into | ? |
÷ | ____ | = | ____ |
× | ____ | = | ____ |
8. A cooking recipes calls for 1/2 cup of butter, among other ingredients. Alison had plenty of every one of the various other ingredients other than the butter. How many batches that the recipe can she make if she has ...
a. 3 cups of butter?
b. 2 ½ cup of butter?
9. Jackie made three apple pies and divided them into twelfths. She plan on serving two slices to each guest. How numerous servings will she gain out that the 3 pies? Hint: draw a picture.
10. How plenty of 2/10-liter servings do you get from 1 liter of juice?
out of 4 liters of juice?
11. As soon as Natalie walk jogging, she jogs because that 1/4 mile, climate walks for 1/4 mile, climate again jogs because that 1/4 mile, and so on. How many such stretches room there for her in a jogging track that is 2 1/2 mile long?
12. Jill renders bead necklaces that should be exactly 24 inch long. She has actually size SS beads, which room 1/8-inch thick, and size S beads, which room 1/4-inch thick.
Bead | Width |
SS | 1/8 in |
S | 1/4 in |
a.How countless beads would certainly be in a necklace made specifically of SS beads?
b.How numerous beads would be in a necklace made specifically of S beads?
c.She also makes a necklace v the sample SS-S-SS-S. How many of each type of bead go she need?
A self-teaching worktext the teaches fractions making use of visual models, a sequel to math Mammoth fountain 1. The publication covers simplifying fractions, multiplication and division of fractions and also mixed numbers, converting fractions to decimals, and also ratios.
See more: How Many Cups In A Pound Of Chicken Breast S Are There In A Cup?
Download ($5.75). Also available as a published copy.