Algebraic ratio problems

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simplest form? (see answers above in black) = = U|N 2 5 59 To complete ratio questions involving algebra, we can use an equivalent fractions approach. Look at these worked examples. Consider these two equivalent ratios. 4:12 = 10:x We can write them as equivalent fractions. 4 10 12 Xx So we can rearrange and solve for x. 10 = 7² 4 x = 30 -X12 Consider these two equivalent ratios. y : 18 = 5:30 We can write them as equivalent fractions. y 5 18 = 30 So we can rearrange and solve for y. 5 y = x18 30 y=3 Copy and complete the questions below. Afterwards mark from the answers on the next slide 1 Solve using equivalent fractions to find the value of each missing variable. (a) 4:10=6:x (c) 10: y = 15:18 (e) 12:16 21:4y (g) 18:5x = 24:40 (b) 6:9=x: 12 (d) y: 15 16:20 (f) 4:14 = 2y : 35 (h) 3x:35 = 24:28 1 Solve using equivalent fractions to find the value of each missing variable. (a) 4:10 = 6:x x = 15 (c) 10: y = 15:18 y = 12 (e) 12:16 21:4y y = 7 (g) 18:5x = 24:40 X = 6 (b) 6:9=x: 12 x=8 (d) y: 15 = 16:20 y = 12 (f) 4:14 = 2y : 35 y = 5 (h) 3x: 35 = 24:28 y = 10 To complete ratio questions involving algebra, we can use an equivalent fractions approach. Look at these worked examples. Consider these two equivalent ratios. y:8 = 3:x We can write them as equivalent fractions. y 3 8 x So we can rearrange and write expressions for x in terms of y or y in terms of x. 3 x=-x8 y 24 x || y y=-x8 37/2 y = 24 x Consider these two equivalent ratios. 7:y=x:2 We can write them as equivalent fractions. 7 x y 2 So we can rearrange and write expressions for x in terms of y or y in terms of x. y y = 7 - x2 X 14 X 7 x=-x2 y 14 y x = Copy and complete the questions below. Afterwards mark in green pen. 1 Using the equivalent fractions method to write an expression for each missing variable in terms of the other (i.e. an expression for x in terms of y and y in terms of x). (a) y: 7 = 5:x (c) 5:y=x: 2 (e) x: 6 = 9:2y (g) 75: 2x = 5y: 12 (b) y: 3 = 5:x (d) 3:y=x:7 (f) 3x: 6-4:y (h) 18:5x = 2y : 45 Copy and complete the questions below. Afterwards mark in green pen. 1 Using the equivalent fractions method to write an expression for each missing variable in terms of the other (i.e. an expression for x in terms of y and y in terms of x). (a) y: 7 = 5:x y = (c) 5:y=x: 2 y 35 X y 10 (e) x: 6 = 9:2y y X 27 X (g) 75: 2x = 5y: 12 90 X x = x = x = x = 35 y 10 y 27 y 90 y (b) y: 3 = 5:x y y = (d) 3:y=x:7 15 X y y 21 (f) 3x:6= 4:y X 8 == X (h) 18:5x = 2y : 45 81 X x = x= 15 y x = 21 y x=- 819 y 81 y To complete ratio questions involving algebra, we can use an equivalent fractions approach. Look at these worked examples. Consider these two equivalent ratios. y: 4 = x:5 We can write them as equivalent fractions. y x 5y = 4x 4 5 So we can rearrange and write expressions for x in terms of y or y in terms of x. y = y = X 45 x4 x = NOTE... x: y = 5:4 y 4 x5 5 4Y ९।४ y = 5|4 To complete ratio questions involving algebra, we must use an equivalent fractions approach. Look at these worked examples. 7x = 4y Consider these two equivalent ratios. X: y = 4:7 We can write them as equivalent fractions. X y 7 So we can rearrange and write expressions for x in terms of y or y in terms of x. 4 -= xy x = 4 x = = y y y = NOTE... x : 4 =y: 7 X -X7 4 74 X ain y 7 814 Copy and complete the questions below. Afterwards mark in green pen. 1 Write each equivalent ratio in the form x : y =:in simplest form. (a) x: 4=y:3 (c) 2x: 3= 3y : 2 (a) x: y = 5:7 (b) x: 6=y:9 2 Write each equivalent ratio in the form x :=y:in simplest form. (c) 2x: 5y = 5:2 (d) 3x: 10 = 5y: 6 (b) x:y=8:12 (d) 6x: 10y = 5:3 Copy and complete the questions below. Afterwards mark in green pen. 1 Write each equivalent ratio in the form x : y =:in simplest form. (a) x: 4=y:3 (c) 2x: 3= 3y : 2 (a) x: y = 5:7 x:y=4:3 (c) 2x: 5y = 5:2 x:y=9:4 x: 5=y: 7 (b) x: 6=y:9 2 Write each equivalent ratio in the form x := y : ☐ in simplest form. x : 25 = y: 4 (d) 3x: 10 = 5y: 6 x:y= 2:3 (b) x: y = 8:12 x : y = 25:9 x: 2=y: 3 (d) 6x: 10y = 5:3 x: 25 = y: 4