Question

Billy is making two 4 by 6 foot paintings for his dad to hang in his office. One painting is of a dinosaur and one is of a mountain. Billy has finished 4/6 of the dinosaur painting. He has also completed 6/8 of the mountain painting. Which painting does Billy have more left to paint? On the lines below explain how you found your answer.​

Answer 1

To determine which painting Billy has more left to paint, we need to compare the fractional parts he has completed for each painting.

For the dinosaur painting, Billy has finished 4/6 of the painting. This means he has 2/6 (or simplified, 1/3) left to paint.

For the mountain painting, Billy has completed 6/8 of the painting. This can be simplified to 3/4.

To compare these two fractions, we need to find a common denominator. The least common multiple of 6 and 4 is 12.

Converting the fractions to have a denominator of 12:

For the dinosaur painting, 1/3 becomes 4/12 (multiply the numerator and denominator by 4).

For the mountain painting, 3/4 becomes 9/12 (multiply the numerator and denominator by 3).

Now we can see that Billy has 4/12 left to paint for the dinosaur painting and 9/12 left to paint for the mountain painting.

Comparing these two fractions, we can conclude that Billy has more left to paint for the dinosaur painting because 4/12 is larger than 9/12.

Therefore, Billy has more left to paint for the dinosaur painting than the mountain painting.

Answer 2

Dinosaur painting

Explanation:

To find out which painting Billy has more left to paint, we need to calculate the area of each painting that is left to paint.

Dinosaur painting:

Total area: 4 feet × 6 feet

= 24 square feet

Area painted: 4/6 × 24 square feet

= 16 square feet

Area left to paint: 24 square feet - 16 square feet

= 8 square feet

Mountain painting:

Total area: 4 feet × 6 feet

= 24 square feet

Area painted: 6/8 × 24 square feet

= 18 square feet

Area left to paint: 24 square feet - 18 square feet

= 6 square feet

Therefore, Billy has more left to paint on the dinosaur painting, because it has 8 square feet left to paint, while the mountain painting only has 6 square feet left to paint.