Review to find two numbers when knowing the sum or difference and the ratio of those two numbers số
Lesson 1 page 176: Write the correct number in the blank
Sum of two numbers 
91 
170 
216 
Ratio of two numbers 
\(\frac{1}{6}\) 
\(\frac{2}{3}\) 
\(\frac{3}{5}\) 
Small number 



Big number 


Solution guide:
 Step 1: Express the small and the large number by an equal number based on the ratio of the two numbers.
 Step 2: Find the total number of equal parts.
 Step 3: Find the value of 1 part by dividing the sum of two numbers by the total number of equal parts.
 Step 4: Find the small number (multiply the partial value by the number of parts of the smaller number).
 Step 5: Find the large number (multiply the partial value by the number of parts of the large number).
Attention : Step 3 and step 4 can be combined into one step.
Solution :
Considering the small number consists of 1 part, the large number consists of 6
$6$such part.
The total number of equal parts is :
1 + 6 =
$7$(part)
The small number is :
91 : 7 × 1 = 13
The big number is:
91 – 13 = 78
Consider the number of children including
$2$equal parts, the large number consists of
$3$such part.
The total number of equal parts is :
2 + 3 = 5 (parts)
The small number is :
170 : 5 × 2 = 68
The big number is:
170−68 = 102
Considering the small number consists of 3 equal parts, the large number consists of
$5$such part.
The total number of equal parts is :
3 + 5 = 8 (parts)
The small number is :
216 : 8 × 3 = 81
The big number is:
216−81 = 135
Sum of two numbers 
91 
170 
216 
Ratio of two numbers 
\(\frac{1}{6}\) 
\(\frac{2}{3}\) 
\(\frac{3}{5}\) 
Small number 
13 
68 
81 
Big number 
78 
102 
135 
Lesson 2 page 176: Write the correct number in the blank
Difference of two numbers 
72 
63 
105 
Ratio of two numbers 
\(\frac{1}{5}\) 
\(\frac{3}{4}\) 
\(\frac{4}{7}\) 
Small number 



Big number 



Solution guide:
 Step 1: Use the ratio of two numbers to represent the large and the small numbers by an equal number of parts.
 Step 2: Find the difference of equal parts.
 Step 3: Find the value of a part by dividing the difference of two numbers by the difference of the equal parts.
 Step 4: Find the small number (multiply the partial value by the number of parts of the smaller number).
 Step 5: Find the big number (take the small number plus the difference of two numbers…).
Attention : Step 3 and step 4 can be combined into one step.
Solution :
Consider the number of children including
$first$part, the large number consists of 5 such parts.
The equal part difference is:
5−1 = 4 (parts)
The small number is :
72 : 4 × 1 = 18
The big number is:
18 + 72 = 90
Consider the number of children including
$3$equal parts, then the large number has 4 such parts.
The equal part difference is:
4 − 3 = 1 (part)
The small number is :
63 : 1 × 3 = 189
The big number is:
189 + 63 = 252
Considering the small number has 3 equal parts, then the large number has 7 such parts.
The equal part difference is:
7 − 4 = 3 (parts)
The small number is :
105 : 3 × 4 = 140
The big number is:
140 + 105 = 245
We have the following table of results:
Difference of two numbers 
72 
63 
105 
Ratio of two numbers 
\(\frac{1}{5}\) 
\(\frac{3}{4}\) 
\(\frac{4}{7}\) 
Small number 
18 
189 
140 
Big number 
90 
252 
45 
Lesson 3 page 176: Two warehouses hold 1345 tons of paddy. Find the number of paddy in each barn, knowing that the number of paddy in the first barn is equal to \(\frac{4}{5}\) the number of paddy in the second barn.
Solution guide:
 Step 1: Draw a diagram: consider the number of paddy in the first warehouse (playing the role of a small number) including
$4$equal parts, the number of paddy in the second barn (which plays the role of a large number) consists of
$5$such part.
 Step 2: Find the total number of equal parts.
 Step 3: Find the value of 1 part by dividing the sum of two numbers by the total number of equal parts.
 Step 4: Find the small number (multiply the partial value by the number of parts of the smaller number).
 Step 5: Find the large number (multiply the partial value by the number of parts of the large number).
Attention : Step 3 and step 4 can be combined into one step.
Solution
We have a diagram:
According to the diagram, the total number of equal parts is:
4 + 5 = 9 (parts)
The number of paddy in the first warehouse is:
1350 : 9 × 4 = 600 (tons)
The number of paddy in the second barn is:
1350 − 600 = 750 (tons)
Answer: First warehouse: 600 tons of paddy;
Second warehouse: 750 tons of paddy.
Lesson 4 page 176: A shop sells 56 boxes of candy and boxes of cakes, where the number of candy boxes is equal to \(\frac{3}{4}\) the number of boxes of cakes. How many boxes of each type did the store sell?
Solution guide:
 Step 1: Draw a diagram: consider the number of candy boxes (as a small number) including
$3$equal parts, the number of cake boxes (playing the role of large numbers) includes
$4$such part.
 Step 2: Find the total number of equal parts.
 Step 3: Find the value of a part by dividing the sum of two numbers by the total number of equal parts.
 Step 4: Find the small number (multiply the partial value by the number of parts of the smaller number).
 Step 5: Find the large number (multiply the partial value by the number of parts of the large number).
Attention : Step 3 and step 4 can be combined into one step.
Solution
We have a diagram:
According to the diagram, the total number of equal parts is :
3 + 4 = 7 (parts)
Number of candy boxes is:
56 : 7 × 3 = 24 (box)
Number of cake boxes is:
56 − 24 = 3
$2$(box)
Answer: Candy: 24 boxes;
Cake: 32 boxes.
Lesson 5 page 176: My mother is 27 years older than me. After 3 years, mother will be 4 times as old as her son. Calculate each person’s current age.
Solution guide:
 Step 1: Find the age difference after 3 years: The age difference does not change over time. Mother is 27 years older than her son, then
$3$next year mom is better than me
$27$year old.
 Step 2: Draw a diagram: Consider the child’s age later
$3$next year (as the small number) includes
$first$part, mother’s age after 3 years (as a large number) consists of 4 such parts.
 Step 3: Find the difference of equal parts.
 Step 4: Find the value of a fraction by dividing the difference of two numbers by the difference of the equal parts.
 Step 5: Find the small number (multiply the partial value by the number of parts of the smaller number)
 Step 6: Find the big number (take the small number plus the difference of two numbers…)
 Step 7: Find the present age, we get the following age
$3$next year minus
$3$year old.
Attention : Step 4 and step 5 can be combined into one step.
Solution
The age difference does not change over time. Mother than me
$27$age, after 3 years, mother will be older than son
$27$year old.
We have a graph of the age after 3 years:
The equal part difference is:
4 − 1 = 3 (parts)
The age of the son after 3 years will be:
27 : 3 = 9 (age)
The present age of the child is:
9 − 3 = 6 (age)
The present age of the mother is:
27 + 6 = 33 (age)
Answer: Mother: 33 years old;
Child: 6 years old.
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