GRADE SIX MATHEMATICS
Hello Boys and Girls! Let’s continue Ratio.
Now work the following. 1. Share 12 marbles in the ratio 1;2 2. Share 30 pins in the ratio 1:4 3. Share 24 oranges in the ratio 1:3 4. Share 40 eggs in the ratio 2:3 5. Share 36 nuts in the ratio 1:2:3
Solve the following problems 6. Jayden and Caden share a reward of $140 in a ratio of 2: 5. What fraction of the total reward does Jayden get? The ratio of girls to boys in a a swimming club was 2: 4. There were 14 girls. How many total members were there in the club? A jar contains 550 beans. Of all the beans, 2/5 are white beans and the rest are navy beans. What is the ratio of white beans to navy beans? Sophia and Isabella share a reward of $117 in a ratio of 1: 8. What fraction of the total reward does Sophia get? 7. 8. 9.
Equivalent Ratio Equivalent ratios (which are, in effect, equivalentfractions) are two ratios that express the same relationship between numbers. We can create equivalent ratios by multiplying or dividing both the numerator and denominator of a given ratio by the same number.
A list of some of the equivalent ratios is as fol lows:
1) 2) 3) 4) 5)
1 : 2, 2 : 4, 4 : 8, 8 : 16, 16 : 32, 32 : 64, 64 : 128, ... 1 : 3, 2 : 6, 3 : 9, 4 : 12, 5 : 15, 6 : 18, 7 : 21, 8 : 24... 1 : 4, 2 : 8, 3 : 12, 4 : 16, 5 : 20, 6 : 24, 7 : 28, ... 1 : 5, 2 : 10, 3 : 15, 4 : 20, 5 : 25, 6 : 30, 7 : 35, ... 1 : 6, 2 : 12, 3 : 18, 4 : 24, 5 : 30, 6 : 36, 7 : 42, ...
The example problems on equivalent ratios are given below:
Example 1: ratios?
Find whether 8 : 18 and 12 : 27 are equivalent
The simplest form of 8 : 18 is obtained by dividing it by 2; i.e. 4 : 9 Also, the simplest form of 12 : 27 is obtained by dividing it by 3, i.e. 4 : 9 Since, both have same simplest form, hence 8 : 18 and 12 : 27 are equivalent ratios.
Example 2: Find two ratios equivalent to 16 : 20 by division method.
Solution: 16 : 20 Dividing both by 2, we get = 8 : 10 Dividing both by 4, we get = 4 : 5 Thus, 16 : 20 = 8 : 10 = 4 : 5 These are required equivalent ratios.
3:
Determine four ratios equivalent Thus, 14 : 8 = 21 : 12 = 28 : 16 = 35 : 20 These are ratios equivalent to 7 : 4. Equivalent ratios word problems Problem 1 : David makes 5 cups of punch by mixing 3 cups of cranberry juice with 2 cups of apple juice. How much cranberry juice and how much apple juice does David need to make four times the original recipe ? Solution : Method 1 : Using table
Step 1 : Make a table comparing the numbers of cups of cranberry juice and apple juice needed to make two times, three times, four times, and five times the original recipe.
Step 2 : The last column of the table shows the numbers of cups of the two juices David needs for four times the original recipe. David needs 12 cups of cranberry juice and 8 cups of apple juice.
Method 2 : Multiplying both terms of the ratio by the same number.
Step 1 : Write the original ratio in fraction form. That is, 3/2 Step 2 : Multiply the numerator and denominator by the same number. To make four times the original recipe, multiply by 4. That is,
To make four times the original recipe, David will need 12 cups of cranberry juice and 8 cups of apple juice.
Problem 2 : Alex makes an alloy by mixing two types of metals, say A and B. To make one unit of alloy, he needs 12 grams of metal A and 17 grams of metal B. If he makes, 5 units of alloy, how many grams of metal A and metal B does he need?
Solution : Step 1 :
Alex needs 12 grams of metal A and 17 grams of metal B to make 1 unit of alloy.
From the above information, the ratio between metal A and metal B to make 1 unit of alloy is Step 2 :
12/17
Since Alex makes 5 units of alloy, we have to multiply the numerator and denominator of the above ratio by 5. Then we have,
(12/17) x (5/5) = 60/85 To make 5 units of alloy, Alex needs 60 grams of metal A and 85 grams of metal B.
Problem 3 : Are these ratios equivalent ? Solution :
From the information we have, we get the following two ratios
To check these two ratios are equivalent, we have to apply cross product rule.
That is, Here, Then, Product of extremes = Product of means — (1)
Then we have, 5 : 3 and 10 : 6
If you have 36 guests, you will need 15 liters of soda. Now work the following: 1. Select three ratios that are equivalent to 7:6
12:14 21:18 42: 36 63:54 2. Select three ratios that are equivalent to 8:20
1: 4 4:10 24:60 2:5 10:24 3. Select two ratios that are equivalent to 2:9
9:2 18:81 12:54 18:4 20:45 4. Select two ratios that are equivalent to 2:12
6:40 12:2 3:24 1:6 8:48 5. According to the chef, perfect cherry pies have a ratio of 240240 cherries to 33 pies. How many cherries does Greg need to make 99 perfect cherry pies? 6. Mabel spends 44 hours to edit a 33 minute long video. She edits at a constant rate. How long does Mabel spend to edit a 99 minute long video? 7. Anna needs 45 kilograms of meat to feed her 2 pet dragons each day. Each pet dragon eats the same amount of meat. How many kilograms of meat does Anna need to feed 4 pet dragons each day? 8. Joseph is making kebabs. He wants each kebab to have 3 pieces of meat and 4 pieces of vegetables. Which of the following could Joseph use to make kebabs without any leftovers?
Choose 3 answers: A 18 pieces of meat and 30 pieces of vegetables B 20 pieces of meat and 32 pieces of vegetables C 30 pieces of meat and 40 pieces of vegetables D 45 pieces of meat and 60 pieces of vegetables E 72 pieces of meat and 96 pieces of vegetables