Who Shaded this?
An array has 3 rows of 5 circles. The first 2 circles in every row are shaded. Write a fraction-times-whole-number expression for the shaded circles. Then find the number shaded.
2/5 x 15 = 6 shaded circles.
Find 3/5 x 10.
6
Without finding the exact product, is 3/8 x 12 greater than or less than 12? Explain.
Less than 12, because 3/8 is less than 1. The product is only part of 12.
Angle A measures 120 degrees. Angle B measures 2/3 as much as angle A. What is the measure of angle B? Show an equation.
2/3 x 120 = 80. Angle B measures 80 degrees.
What multiplication expression represents 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8? Find its value.
6 x 1/8, or 1/8 x 6. The value is 6/8 = 3/4.
An array has 4 rows of 4 circles. Three circles in each row are shaded. Write a fraction-times-whole-number expression for the shaded circles. Then find the number shaded.
3/4 x 16 = 12 shaded circles.
Find 1/4 x 7
7/4, or 1 3/4
Without finding the exact product, is 7/5 x 6 greater than or less than 6? Explain.
Greater than 6, because 7/5 is greater than 1.
A trampoline park sold 84 tickets. Of those tickets, 5/7 were for children. How many tickets were for children? Show an equation.
5/7 x 84 = 60 tickets for children.
To find 2/7 of 14, a student first calculates 14 divided by 7. What does that quotient represent? What should the student do next?
14 divided by 7 = 2 is the value of 1/7 of 14. Multiply 2 by 2 to find 2/7 of 14 = 4.
An array has 5 rows of 6 circles. One circle in every row is shaded. What fraction of all the circles is shaded? How many circles are shaded?
1/6 of the circles; 1/6 x 30 = 5 shaded circles.
Find 5/6 x 9
45/6 = 15/2 = 7 1/2
Fill in the comparison symbol: 4/9 x 15 __ 15. Explain using the fraction's numerator and denominator.
<. Since 4 < 9, the fraction 4/9 is less than 1, so the product is less than 15.
A trampoline park sold 84 tickets. Of those tickets, 5/7 were for children, and all the others were for adults. How many adult tickets were sold? Show your reasoning.
2/7 x 84 = 24 adult tickets, or 84 - 60 = 24 adult tickets.
A student writes 3/5 x 10 = 30/50. Explain the error and give the correct product.
The student multiplied both the numerator and denominator by 10. Multiplying by the whole number 10 means multiplying the numerator by 10 and keeping the denominator: 30/5 = 6.
An array has 3 rows of 7 circles. Four circles in every row are shaded. Write an expression for the number shaded. How many circles are NOT shaded?
4/7 x 21 = 12 shaded; 21 - 12 = 9 unshaded circles.
Find 7/4 x 3
21/4, or 5 1/4
Put these expressions in order from least to greatest without finding exact products: 11/6 x 4, 4/9 x 4, and 1 x 4. Explain.
4/9 x 4 < 1 x 4 < 11/6 x 4. The multipliers are less than 1, equal to 1, and greater than 1.
Angle C measures 150 degrees. Angle D measures 3/5 as much as angle C. How many degrees SMALLER is angle D than angle C?
Angle D is 3/5 x 150 = 90 degrees. The difference is 150 - 90 = 60 degrees.
Blake finds 3/4 x 36 = 27. He is surprised because he thinks multiplication always produces a number greater than both factors. Explain why 27 is reasonable.
3/4 is less than 1, so taking 3/4 of 36 gives only part of 36. One fourth of 36 is 9, so three fourths is 27, which is less than 36.
A set of 35 counters is divided into 5 equal groups. You select 3 groups. Draw a tape diagram showing the total, the equal groups, and the selected amount. Write and solve an equation.
The tape shows 35 in all, 5 equal parts of 7, and 3 selected parts. 3/5 x 35 = 21 counters.
Find BOTH products: 11/8 x 5 and 4/3 x 5.
55/8 = 6 7/8; 20/3 = 6 2/3
A student says, '8/5 x 4 is less than 4 because multiplying by any fraction makes a number smaller.' Correct the claim and find the product.
Only multiplying a positive number by a positive fraction less than 1 makes it smaller. Since 8/5 > 1, the product is greater than 4. 8/5 x 4 = 32/5 = 6 2/5.
A park sold 96 tickets on Friday and 84 tickets on Saturday. On Friday, 3/4 were children's tickets. On Saturday, 5/7 were children's tickets. Which day had more children's tickets, and how many more?
Friday: 3/4 x 96 = 72. Saturday: 5/7 x 84 = 60. Friday had 12 more children's tickets.
Use TWO different methods to find 3/8 x 12. One method must use a unit fraction or a model. Explain why both methods give the same value.
Method 1: (3 x 12)/8 = 36/8 = 4 1/2. Method 2: 1/8 of 12 = 12/8 = 1 1/2; three of those parts total 4 1/2. A tape diagram may show 12 split into 8 equal parts with 3 selected. Both methods find three eighths of 12.