Question paper, Set 6

A variable (or literal) can take various numerical values. A constant has a fixed value.

$-21$, $29$ and $\displaystyle \frac{4}{7}$ have fixed values, so they are constants.

$c$ can take various values, so it is the variable.

Answer: $c$

Variables can take various numerical values: $a$, $n$ and $q$.

Constants have a fixed value: $\displaystyle -\frac{3}{4}$, $25$ and $\displaystyle -\frac{2}{3}$.

Answer: (i) $a$, $n$, $q$ (ii) $\displaystyle -\frac{3}{4}$, $25$, $\displaystyle -\frac{2}{3}$

$y = 1 \times y$

Answer: $y = 1 \times y$

(i) $45$ more than $c$: add $45$ to $c$. $c + 45$

(ii) Take $6m$ away from $15$. $15 - 6m$

Answer: (i) $c + 45$, (ii) $15 - 6m$

(i) $4$ times $b$ is $4b$; $9$ times $x$ is $9x$. Add $4b$ to $9x$: $9x + 4b$

(ii) $r$ divided by $19$ is $\displaystyle \frac{r}{19}$

(iii) $34$ more than $b$: add $34$ to $b$. $b + 34$

(iv) Take $4x$ away from $29$. $29 - 4x$

(v) Multiply: $24 \times y = 24y$

Answer: (i) $9x + 4b$, (ii) $\displaystyle \frac{r}{19}$, (iii) $b + 34$, (iv) $29 - 4x$, (v) $24y$

(i) Half of $t$ is $\displaystyle \frac{t}{2}$

(ii) Half of $b$ is $\displaystyle \frac{b}{2}$. $12$ less than it: take away $12$. $\displaystyle \frac{b}{2} - 12$

Answer: (i) $\displaystyle \frac{t}{2}$, (ii) $\displaystyle \frac{b}{2} - 12$

Rule: $-1 \times a = -a$

So $-1 \times yz = -yz$: the box is $-1$.

Answer: $-1$

(i) Rule $1 \times a = a$, so $1 \times xz = xz$

(ii) Rule $\displaystyle \frac{a}{1} = a$, so $\displaystyle \frac{n}{1} = n$

(iii) Rule $\displaystyle \frac{a}{-1} = -a$, so $\displaystyle \frac{bc}{-1} = -bc$

Answer: (i) $xz$, (ii) $n$, (iii) $-bc$

A term is made from constants and variables by multiplication (or) division only.

$15b - x$ and $8q - t$ use $+$ (or) $-$, so they are not terms.

Terms: $30$, $\displaystyle \frac{3n}{b}$ and $-7mnp$.

Answer: $30$, $\displaystyle \frac{3n}{b}$, $-7mnp$

$20xy = 20 \times x \times y$

Each numerical (or) literal value in the product is a factor: $20, x, y$.

Answer: $20xy = 20 \times x \times y$; factors $20, x, y$

(i) $2z = 2 \times z$, so the coefficient is $2$.

(ii) $12pz = 12p \times z$, so the coefficient is $12p$.

(iii) $17cz = 17c \times z$, so the coefficient is $17c$.

Answer: (i) $2$, (ii) $12p$, (iii) $17c$

$\displaystyle -\frac{x}{8} = -\frac{1}{8} \times x$

So the coefficient of $x$ is $\displaystyle -\frac{1}{8}$.

Answer: $\displaystyle -\frac{1}{8}$

(i) $\displaystyle -\frac{7}{5}np$, $12pn$: the same literal factors $np$ ($pn = np$), so like terms.

(ii) $-11py$ has literal factors $py$, $-11yz$ has literal factors $yz$: different, so unlike terms.

Answer: (i) Like, (ii) Unlike

Like terms have the same literal factors.

Literal factor $np$: $-8np$, $-6np$ and $-15np$.

Literal factor $c$: $-8c$ and $-13c$.

Literal factor $r$: $5r$ and $15r$.

Answer: $-8np$, $-6np$, $-15np$; $-8c$, $-13c$; $5r$, $15r$

$27np + 17np = (27 + 17)np$

$= 44np$

Answer: $44np$

(i) $15z + 24z = (15 + 24)z$ $= 39z$

(ii) $2xy + 29xy = (2 + 29)xy$ $= 31xy$

Answer: (i) $39z$, (ii) $31xy$

Bring the like terms together and add.

$11y + 18q + 5t + 4y + 3q + 17t = (11y + 4y) + (18q + 3q) + (5t + 17t)$

$= (11 + 4)y + (18 + 3)q + (5 + 17)t$

$= 15y + 21q + 22t$

Answer: $15y + 21q + 22t$

(i) $-26a + 11a = (-26 + 11)a = -15a$

(ii) $-4a - 21a = (-4 - 21)a = -25a$

(iii) $3a - 22a = (3 - 22)a = -19a$

Answer: (i) $-15a$, (ii) $-25a$, (iii) $-19a$

(i) $-8xy + 18xy = (-8 + 18)xy = 10xy$

(ii) $4xy - 12xy = (4 - 12)xy = -8xy$

(iii) $-15xy + 9xy = (-15 + 9)xy = -6xy$

(iv) $-14pr - 29pr = (-14 - 29)pr = -43pr$

(v) $20pr - 18pr = (20 - 18)pr = 2pr$

Answer: (i) $10xy$, (ii) $-8xy$, (iii) $-6xy$, (iv) $-43pr$, (v) $2pr$

Bring the like terms together, then add (or) subtract the numbers.

$8m - 20pr + 14y - 8pr - 10m + 18y - 15pr = (8m - 10m) + (-20pr - 8pr - 15pr) + (14y + 18y)$

$= (8 - 10)m + (-20 - 8 - 15)pr + (14 + 18)y$

$= -2m - 43pr + 32y$

Answer: $-2m - 43pr + 32y$