Here are the step-by-step solutions for each problem on the worksheet.
1 a.
*
Step 1: Find the number of black horses. We know there are 52 horses in total and 12 are white. So, we subtract the white horses from the total: $52 - 12 = 40$ black horses.
*
Step 2: Write the ratio of white to black horses. That is 12 to 40.
*
Step 3: Simplify the ratio. Both numbers can be divided by 4.
* $12 \div 4 = 3$
* $40 \div 4 = 10$
* The simplified ratio is
3:10.
2 a.
*
Step 1: Find the total number of triangles. Add the blue triangles and yellow triangles together: $5 + 80 = 85$ total triangles.
*
Step 2: Write the ratio of blue triangles to all triangles. That is 5 to 85.
*
Step 3: Simplify the ratio. Both numbers end in 5 or 0, so they can be divided by 5.
* $5 \div 5 = 1$
* $85 \div 5 = 17$
* The simplified ratio is
1:17.
3 a.
*
Step 1: Find the total number of shapes. Add the hearts and circles together: $22 + 76 = 98$ total shapes.
*
Step 2: Write the ratio of circles to all shapes. That is 76 to 98.
*
Step 3: Simplify the ratio. Both numbers are even, so divide by 2.
* $76 \div 2 = 38$
* $98 \div 2 = 49$
* Check if it simplifies further: 49 is $7 \times 7$, but 38 is not divisible by 7. So, it is fully simplified.
* The simplified ratio is
38:49.
4 a.
*
Step 1: Identify the numbers. There are 14 blue triangles and 18 yellow triangles.
*
Step 2: Write the ratio of yellow to blue. Be careful with the order! It asks for yellow first. That is 18 to 14.
*
Step 3: Simplify the ratio. Both numbers are even, so divide by 2.
* $18 \div 2 = 9$
* $14 \div 2 = 7$
* The simplified ratio is
9:7.
5 a.
*
Step 1: Identify the numbers. There are 6 blue triangles and 42 yellow triangles.
*
Step 2: Write the ratio of yellow to blue. Again, yellow comes first. That is 42 to 6.
*
Step 3: Simplify the ratio. Both numbers are divisible by 6.
* $42 \div 6 = 7$
* $6 \div 6 = 1$
* The simplified ratio is
7:1.
6 a.
*
Step 1: Find the total number of children. Add the boys and girls together: $63 + 27 = 90$ total children.
*
Step 2: Write the ratio of boys to all children. That is 63 to 90.
*
Step 3: Simplify the ratio. Both numbers are divisible by 9 (because $6+3=9$ and $9+0=9$).
* $63 \div 9 = 7$
* $90 \div 9 = 10$
* The simplified ratio is
7:10.
Final Answer:
1 a. 3:10
2 a. 1:17
3 a. 38:49
4 a. 9:7
5 a. 7:1
6 a. 7:10
Parent Tip: Review the logic above to help your child master the concept of ratios worksheet grade 6.
