Question

Mrs. Suarez bakesa cake to be serve during her bday celebration.she has 2 1/5 of flour and then she bought 4/5 kg more.if she uses 3/4 kg for each cake,how many cakes can she make?

Answer 1

Answer:

these work before moving on:

(a) 3a + 12b – 5a + 7b – 2a = – 4a + 19b

(b) x² + 5x – 5 + 4x² – 3x + 5 = 5x² + 2x (these two terms can not be added as one is x and the other is x²)

(c) 2p + 3pq – 5pq² + 6p – pq = 8p + 2pq – 5pq²

Practice Questions

Work out the answer to each question then click on the button marked to see if you are correct.

Simplify these expressions by collecting like terms:

(a) 3p + 6q – 5p + 3q

(b) x3 – 4x2 + 7x – 3 + 7x2 – 9x + 1

(c) ab2 + 3ab - 3a + 2ab2 - 5ba + 4a

Laws of Indices

Rules to learn

positive powers an means multiply together n lots of a

e.g. a5 = a × a × a × a × a

multiplying powers If the bases are the same then you add the powers: am × an = a(m + n)

e.g. x5 × x3 = x8

dividing powers If the bases are the same then you subtract the powers: am ÷ an = a(m – n)

e.g. y2 ÷ y6 = y– 4

This also works for powers in fractions: e.g. p7 = p3 p4

powers of powers The powers are multiplied: (am)n = a(mn)

e.g. (z2)5 = z10

special powers a1 = a and a0 = 1

e.g. b4 ÷ b3 = b1 = b

e.g. d 3 × d – 3 = d 0 = 1

multiplying terms To multiply terms, multiply the coefficients to get the new coefficient then multiply each letter in turn:

e.g. 3x2 × 5x3 = 15x5

e.g. 4xy 2 × x3 × 3x

Answer 2

Given:

Mrs. Suarez bakes a cake to be served during her bday celebration. She has 2 1/5 of flour and then she bought 4/5 kg more. If she uses 3/4 kg for each cake, how many cakes can she make?

To find:

How many cakes can she make?

Solution:

The quantity of flour Mrs. Suarez had = $2\frac{1}{5} \:kg = \frac{11}{5} \:kg$

The quantity of flour she bought more = $\frac{4}{5} \:kg$

∴ The total quantity of flour she had for baking a cake is,

= $\frac{11}{5} + \frac{4}{5}$

= $\frac{15}{5}$

= $3 \:kg$

The quantity of flour she uses for baking 1 cake = $\frac{3}{4} \:kg$

Now,

The no. of cakes she can make with the total quantity of cake is,

= $\frac{\big{3}}{\big{\frac{3}{4} }}$

= $3 \times \frac{4}{3}$

= $\bold{4}$

Thus, Mrs. Suarez can make 4 cakes.

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