In 1 through 6, find each sum. Simplify, if possible. Estimate for reasonableness.
1. 7
__2
3
+ 8
__5
6
2. 4
__3
4
+ 2
__2
5
3. 11
___9
10
+ 3
___1
20
4. 7
__6
7
+ 5
__2
7
5. 5
__8
9
+ 3
__1
2
6. 21
___ 11
12
+ 17
__2
3
7. Number Sense Write two mixed numbers that have a sum of 3.
Fractions don't format well here. Try using a/b for fractions.
I'll do #1 and yo can post your own answers for the others, which we will be happy to check.
#1.
7 2/3 + 8 5/6
One way is to add the whole numbers, then add the fractions:
7+8 + 2/3 + 5/6
15 + 2/3 + 5/6
Now, set the fractions over a common denominator:
15 + 4/6 + 5/6
15 + 9/6
Now reduce the improper fraction to a mixed number:
15 + 6/6 + 3/6
15 + 1 + 3/6
16 1/2
Another way is to make everything into fractions first:
7 2/3 + 8 5/6
21/3 + 2/3 + 48/6 + 5/6
42/6 + 4/6 + 48/6 + 5/6
99/6
96/6 + 3/6
16 1/2
To find each sum in the given equations, you need to add the fractions together. Let's break down the steps for each sum:
1. 7/3 + 8/6:
First, find a common denominator for the fractions, which is 6.
Multiply the numerator and denominator of 7/3 by 2, which gives us 14/6.
Rewrite the equation: 14/6 + 8/6.
Add the numerators: 14 + 8 = 22.
Keep the denominator the same: 22/6.
Simplify, if possible: 22 divided by 2 is 11, and 6 divided by 2 is 3.
The simplified fraction is 11/3.
2. 4/4 + 2/5:
The denominators are already the same, so we can add the numerators directly.
Add 4 + 2 = 6.
Keep the denominator the same: 6/4.
Simplify the fraction: 6 divided by 2 is 3, and 4 divided by 2 is 2.
The simplified fraction is 3/2.
3. 11/10 + 3/20:
The denominators are not the same, so we need to find a common denominator.
Multiply the numerator and denominator of 11/10 by 2, which gives us 22/20.
Rewrite the equation: 22/20 + 3/20.
Add the numerators: 22 + 3 = 25.
Keep the denominator the same: 25/20.
Simplify the fraction: 25 divided by 5 is 5, and 20 divided by 5 is 4.
The simplified fraction is 5/4.
4. 7/7 + 5/6:
The denominators are not the same, so we need to find a common denominator.
Multiply the numerator and denominator of 7/7 by 6, which gives us 42/42.
Rewrite the equation: 42/42 + 5/6.
Add the numerators: 42 + 5 = 47.
Keep the denominator the same: 47/42.
Simplify the fraction: 47 divided by 7 is 6, and 42 divided by 7 is 6.
The simplified fraction is 6/6, which is equal to 1.
5. 5/9 + 3/12:
The denominators are not the same, so we need to find a common denominator.
Multiply the numerator and denominator of 5/9 by 4, which gives us 20/36.
Rewrite the equation: 20/36 + 3/12.
Add the numerators: 20 + 3 = 23.
Keep the denominator the same: 23/36.
6. 21/12 + 17/3:
The denominators are not the same, so we need to find a common denominator.
Multiply the numerator and denominator of 21/12 by 3, which gives us 63/36.
Rewrite the equation: 63/36 + 17/3.
Multiply the numerator and denominator of 17/3 by 12, which gives us 204/36.
Add the numerators: 63 + 204 = 267.
Keep the denominator the same: 267/36.
Now, let's answer the next question:
7. To write two mixed numbers that have a sum of 3, we can try different combinations. One example would be 1 1/2 and 1 1/2. If we add 1 1/2 + 1 1/2, we get 3.