In this lesson us solve fraction divisions by thinking how many times the divisor "fits" or "goes into" the dividend. Because that example, the portion 1/4 goes into five 20 times, therefore 5 ÷ (1/4) = 20. The lesson has actually lots that exercises with visual models and also many indigenous problems. The vault lesson had actually to do with splitting fractions by totality numbers.In the video, I explain two different division situations where we don"t need to use the "rule" or faster way for fraction division, yet instead can use mental math. The first is when a fraction is split by a totality number. The 2nd is as soon as the answer to a fraction division is a entirety number.
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How countless times go one thing fit into another?You can constantly write a division from this situation. Think: “How numerous times does the divisor get in the dividend?” | |||
How plenty of times does | go into | ? |
Eight times. We deserve to 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. Compose a division. Then write a multiplication that checks her division.
a.How plenty of times does |
| go into | ? |
2 ÷ | 1 3 | =_____ |
Check: ____ × | 1 3 | = |
go into | ? |
1 ÷ | 1 4 | = _____ |
Check: ____ × | 1 4 | = |
go right into | ? |
6 ÷ | 1 3 | =____ |
go into | ? |
5 ÷ | 1 4 | =____ |
e. How plenty of times does | go right into | ? |
____ | ÷ | = |
go into | ? |
____ | ÷ | ____ | = |
1 6 | go into 2? |
____ | ÷ | ____ | = |
1 5 | go 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 splitting a totality number through a unit fraction! | ÷ | 1 4 | |
↓ | ↓ | ||
5 | × | 4 | = 20 |
÷ | 1 8 | ||
↓ | ↓ | ||
3 | × | 8 | = 24 |
÷ | 1 7 | ||
↓ | ↓ | ||
9 | × | 7 | = 63 |
Why go it occupational that way? because that example, think about the trouble 5 ÷ (1/4). Due to the fact that 1/4 goesinto 1 exactly 4 times, that must enter 5 specifically 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. Create a department for each word problem, and solve. Perform not write simply the answer.
a. How many 1/2-meter pieces can you reduced from a roll of string the is 6 meter long? |
b. How numerous 1/4-cup servings deserve to you get from 2 cup of almonds? |
c. Ben has tiny weights that sweet 1/10 kg each. How numerous of those would he should make 5 kg? |
d.An eraser is 1/8 inch thick. How numerous erasers have the right to be stacked into a 4-inch high box? |
a. 2 ÷ | 1 2 | = |
b. 5 ÷ | 1 3 | = |
6. These divisions are no as basic as the ahead ones, however they are not difficult either. Again, think how plenty of times the divisor goes right into the dividend. The pictures can help.
a. 4 ÷ | 2 3 | = |
4 5 | = |
5 6 | ÷ | 1 6 | = |
6 10 | = |
5 9 | ÷ | 4 9 | = |
4 8 | ÷ | 5 8 | = |
7. Write a department and solve. Write additionally a multiplication to check your division.
a. How countless times does | go into | ? |
÷ | ____ | = | ____ |
× | ____ | = | ____ |
go into | ? |
÷ | ____ | = | ____ |
× | ____ | = | ____ |
go into | ? |
÷ | ____ | = | ____ |
× | ____ | = | ____ |
go into | ? |
÷ | ____ | = | ____ |
× | ____ | = | ____ |
8. A recipe calls because that 1/2 cup the butter, among other ingredients. Alison had plenty of all of the other ingredients other than the butter. How numerous batches the the recipe have the right to she make if she has actually ...
a. 3 cup of butter?
b. 2 ½ cups of butter?
9. Jackie made three apple pies and divided them right into twelfths. She plans on serving 2 slices to each guest. How many servings will she get out of the 3 pies? Hint: draw a picture.
10. How plenty of 2/10-liter servings execute you acquire from 1 liter that juice?
out of 4 liters the juice?
11. Once Natalie goes jogging, she jogs for 1/4 mile, climate walks for 1/4 mile, climate again jogs for 1/4 mile, and also so on. How countless such stretches space there for she in a jogging track that is 2 1/2 mile long?
12. Jill makes bead necklaces that have to be specifically 24 customs long. She has 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 many beads would be in a necklace made solely of SS beads?
b.How numerous beads would be in a necklace made solely of S beads?
c.She also makes a necklace v the sample SS-S-SS-S. How numerous of each sort of bead does she need?
A self-teaching worktext that teaches fractions making use of visual models, a sequel to mathematics Mammoth fractions 1. The book covers simple fractions, multiplication and division of fractions and mixed numbers, converting fractions to decimals, and also ratios.
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Download ($5.75). Also accessible as a published copy.